The doctored message is being sent as an image, not a link to a tweet.
“A man was murdered by British Police in Broad daylight,” it says.
Labour confirmed to The Independent that the tweet was fake.
But responses to the image on Twitter suggested users had been duped by the fakery.
“This is what you get if this man becomes PM. God help us,” tweeted one.
Mr Corbyn’s real response to the attack expressed thanks for the efforts of emergency workers.
“Shocking reports from London Bridge. My thoughts are with those caught up in the incident.
“Thank you to the police and emergency services who are responding,” the Labour leader said.
In a later statement announcing that his party would suspend general election campaigning in the capital on Friday, he added: ”We owe a deep debt of gratitude to our police and emergency services, and the brave members of the public who put themselves in harm’s way to protect others.”