The environmental artwork sprung up on a wall in Marble Arch around the time the demonstrators gathered nearby to celebrate the closing of their spell of disruption in central London.
While there is no confirmation the piece is by the famed artist, it does bear a similar stencilled style.
It shows a child clutching an Extinction Rebellion sign while crouching near a plant shoot emerging from the earth.
"From this moment despair ends and tactics begin," accompanying words say.
Skeena Rathor, vision co-ordinator for the activists also known as XR, told the crowd in Speaker's Corner in Hyde Park on Thursday that the event marked a "pause" in their protests.
But on Friday morning, several defiant Extinction Rebellion protesters remained at Marble Arch having slept overnight in tents.
Police officers circulated the area, still occupied by a few flags and signs, but the bulk of the protest had gone as cleaners moved in to wipe away chalk messages on the pavement.
Extinction Rebellion supporter Calvin Benson, 48, from north west London, said: "I wanted to come down to protect this artwork because it needs to be preserved, we've just had an historical event over the last 10 days in London.
"This artwork represents the will of the people that were here and the people of the nation."
When asked how sure he was the painting is one of Banksy's, he said: "One hundred per cent its a Banksy, it's already been confirmed by street artists and the whole community knows about this. Most of them had been down here.
"Read the message, he's a supporter of Extinction Rebellion."
Some of those still camped at Marble Arch last night said it happened between 7.30pm and 10pm, but did not see anything.
Steve Jones, 53, from Holland Park in west London, said: "I was right under the nose of it all, but I didn't see a single thing. I returned from an Extinction Rebellion meeting and it was there, it just appeared.
"A man we met last night said he had been taking photographs of Banksy's work after it's done, and this ticks all the boxes.
"It shows a message of hope and desire for the future against the tyranny we are held under."