The Year 8 pupil, thought to be 12 or 13, was travelling with a friend on a bus on Tuesday morning when he got off before his usual stop, his headteacher said.
City of London Police said that despite an intensive search by officers and helicopter and marine units, the boy had not yet been found.
Matt Jones, executive principal of the boy’s school, Ark Globe Academy, in Southwark, south London, wrote in a letter to parents that the boy did not arrive at school.
He was in full school uniform but got off the bus near the bridge, earlier than his usual stop near the school in Elephant and Castle.
He then “fell” into the River Thames, Mr Jones said.
Police confirmed they were leading an investigation into a missing person, “linked to an incident where a child fell into the river from Tower Bridge”.
A witness waded into the water to try to save the boy but could retrieve only his schoolbag as he disappeared under the water, The Sun reports.
Another witness reportedly said: “We all heard him screaming for help, and then a woman who was just walking past with her boyfriend grabbed a float and jumped into the river.
“She said ‘why isn’t anybody helping him’ before jumping in herself. All she could bring back was his school jacket and his bag.
“I saw police going through the bag and it had his school books and stationery in it. He was clearly very young.”
Mr Jones said in his letter: “It is with worry that I share news about [the pupil’s name], a Year 8 student at Ark Globe Academy.
“On the morning of Tuesday 20 April, [he] did not make his way into school, despite travelling on a bus with a friend in full school uniform.
“He got off the bus near Tower Bridge before his usual bus stop nearest to Ark Globe Academy and fell into the River Thames.
“At this moment in time, police are treating this case as a ‘missing persons’ incident.”
Mr Jones said in a statement on Friday: “This is obviously distressing news for the young person’s family, friends and the wider Ark Globe community.
“As a school community, we are dealing with this sensitively so as not to compromise the integrity of the police investigation and we wish to respect the privacy of the family while the investigation is ongoing.
“Our hopes and prayers are with the family at this very difficult time.”
A City of London Police spokesperson said the force were working with the Metropolitan Police as part of the missing person investigation.
The spokesperson said: “We believe this is linked to an incident where a child fell into the Thames from Tower Bridge.
“Despite an intensive search by City of London Police, the police helicopter and marine units, this person has not yet been found.
“We ask anyone who witnessed anything on Tuesday April 20 at 8.09am, to call us on 020 7601 2999.”