Steve Sinnott, general secretary of the National Union of Teachers, has written to the anti-war MP in response to his description of schools in Tower Hamlets as the worst in the country.
The union leader said Mr Galloway's comments would demoralise school staff and mislead parents about the quality of education in the London borough, which has been rated as good by inspectors.
Primary pupils' test results in Tower Hamlets are at the national average, despite the fact that the area is one of the most socially deprived in the country.
The proportion of pupils gaining five or more A*-C grade GCSEs has increased from 26 per cent in 1998 to 48 per cent last year, one of the biggest rises in England.
Mr Galloway, who stood for the Respect party, made his remarks during a bitter election battle against Oona King, the former Labour MP in Bethnal Green and Bow.
Mr Galloway won the seat, which has a large Muslim population, by a majority of 823 in a 26 per cent swing from Labour.
Last week, Mr Galloway appeared before the US Senate to defend himself against charges that he had accepted oil from Saddam Hussein, the former Iraqi dictator.
Mr Sinnott said: "George Galloway should show respect for teachers and schools in Tower Hamlets.
"Schools in the borough offer remarkably high-quality education, according to the Office for Standards in Education."
A spokesman for Mr Galloway said: "It is not teachers' fault, but it is our view that the local education authority has badly let down the people of Tower Hamlets."
He said Mr Galloway planned to hold a local forum with teachers, parents and others next month to discuss the best way to improve the situation in the borough.