Brian Jones, head of Archbishop Tenison's secondary school in Oval, south London, wrote to staff saying they would lose retention bonuses worth pound;400 to pound;1,200 if they missed a day by taking part in any industrial action.
The head's actions were condemned by the National Union of Teachers at a rally held in the nearby Oval cricket ground, which was attended by around 8,000 people.
Alex Penny, secretary of the union's Tower Hamlets branch, told the crowd that Archbishop Tenison's had "tried to intimidate teachers, and stop them taking the action". The all-boys school closed after 18 staff decided to strike.
Ray Sirotkin, Lambeth NUT secretary, said teachers at Archbishop Tenison's felt the head's letter presented a bribe and threat, and that a similar letter at the start of the year had put staff off taking part in the first one-day London strike in March.
He said that the 1996 Employment Rights Act did not give headteachers the right to withhold bonuses from staff who took part in industrial action.
Teachers said they had been told to see the head if they were planning to take part in the strike.
Mr Jones, the head, said: "If teachers have complaints about intimidation, they haven't made them to me."
He referred further questions to Ian Coupe, Greater London officer of the National Association of Head Teachers, who said Mr Jones was satisfied his letter was lawful and consistent with the teachers' pay and conditions document.