The Football Association also said players would wear black armbands for the match at Wembley on Friday.
More than 1,200 people have been killed after Palestinian militant group Hamas launched a series of attacks on Israel.
Israel then launched air strikes on Gaza and stopped food, water, fuel and medicine going into the territory.
More than 1,300 people have been killed in Gaza since the retaliatory strikes, with 338,000 displaced.
"On Friday evening, we will remember the innocent victims of the devastating events in Israel and Palestine," the FA said in a statement.
"Our thoughts are with them, and their families and friends in England and Australia and with all the communities who are affected by this ongoing conflict.
"We stand for humanity and an end to the death, violence, fear and suffering."
It said only "flags, replica kits and other representations of nationality for competing nations" would be allowed inside Wembley for the match against Australia and Tuesday's Euro 2024 qualifier against Italy.
A Football Australia spokesperson told BBC Sport: "The English Football Association consulted with Football Australia on their proposed plans and public statement, which we are aligned on."
The English FA statement did not include mention of the Wembley arch.
BBC Sport reported on Wednesday that the governing body was unlikely to illuminate the arch in the colours of the Israel flag because of fears of a backlash from some communities.
Senior officials at the FA were understood to be wary of a perception they might be taking sides in the Middle East conflict.
Former FA chairman David Bernstein, who is Jewish, has said he is "deeply disappointed" but "not at all surprised" at the decision not to light the arch in the colours of the Israel flag.
Speaking to Jewish News, Bernstein added: "It is a tardy reaction to the horrors in Israel. This is a continuation of the double standards that football has shown in dealing with recent tragedies."
Uefa chief expresses 'profound sorrow' to Israel
The Israel-Palestinian conflict explained
What is happening in Israel and Gaza and why now?
Officials from the Department for Culture, Media and Sport wrote to major sports governing bodies on Wednesday asking them to mark the attacks in Israel with shows of support for the victims.
"In the light of the attacks in Israel, on behalf of the secretary of state we would encourage you to mark the events appropriately in line with previous events where sport has come together," the letter read.
Last year, the FA lit Wembley's arch in the blue-and-yellow colours of the Ukraine flag in solidarity with the country after it was invaded by Russia.
The arch was also illuminated in the colours of the France flag in 2015 in tribute to the people killed in attacks in Paris, and the colours of the Belgium flag adorned the arch in 2016 in respect of the victims of the Brussels bombings.
The Rugby Football League has been holding talks to decide how to mark the events before Saturday's Grand Final between Wigan Warriors and Catalans Dragons at Old Trafford.
It is understood to be planning to pay tribute to victims with a show of support before the match.
The England and Wales Cricket Board said it deplored "the appalling loss of innocent life following recent events in Israel and Palestine".
It added: "Our thoughts and prayers are with the families and friends of all the innocent victims, and those who are still missing, as well as the communities who are affected.
"While sport seems trivial compared to the harrowing scenes we have all watched, it is also an opportunity for people to come together and remind ourselves that there's far more that brings us together, than divides us. We should now all unify in our hope for peace."
The Premier League said it has been "shocked and saddened by the escalating crisis in Israel and Gaza and strongly condemns the horrific and brutal acts of violence against innocent civilians".
"We hope for peace, and our heartfelt sympathies are with the victims, their families and the communities impacted," it added.
The Women's Super League said it will "remember the innocent victims of the devastating events in Israel and Palestine" and requested that clubs wear black armbands and observe a period of silence at matches this weekend.
In a joint statement with the Women's Championship and Women's National League, the WSL added: "Our thoughts are with them, their families and friends and with all the communities who are affected by this ongoing conflict."
The EFL expressed concern about what it described as "shocking and devastating events".
Players, managers and match officials in the EFL will wear black armbands this weekend, while the same will occur at Premier League fixtures taking place from 21 to 23 October.
A moment's silence will also be observed at Premier League matches next week, with no games in the top flight taking place this weekend due to the international break.
Both organisations are making a donation to the British Red Cross to help those in urgent need.
Uefa president Aleksander Ceferin, meanwhile, expressed "profound sorrow" about "the tragic acts of violence" in Israel.
Ceferin made his remarks on behalf of the European football community in a letter sent to the chairman of the Israel Football Association.
On Wednesday, the Philadelphia Phillies baseball team lit their stadium in blue and white "to show our unwavering support for the people of Israel".
