Lyon have blamed the sale on Bafetimbi Gomis' refusal to leave the Stade de Gerland.
Lyon are listed on the Paris Stock Exchange and had to sell at least one player by the end of Sunday to be able to report balanced yearly results.
Lyon were hoping that player would be Gomis, who was heavily linked with Swansea and Cardiff, as well as Shakhtar Donetsk, and has one year left on his contract.
However, a possible move for Gomis has stalled and, according to the club, he "has not gone yet", leaving them little choice but to sell the 17-year-old striker.
"Having not been able to complete the move of any player approached for a transfer by 30 June, notably Bafetimbi Gomis, the club considered Monaco's offer for Anthony Martial," a statement from Lyon read.
"The club completed Anthony Martial's move for five million euros plus an important share on a future transfer."
Monaco were delighted by the acquisition, believing the striker will play a big part in the club's future.
Technical director Riccardo Pecini said: "We are very happy that Anthony has joined us."