The Colombia international damaged the anterior cruciate ligament in his left knee during Monaco's Coupe de France victory over Monts d'Or Azergues in January.
Falcao missed the remainder of the domestic season, as well as his country's World Cup campaign in Brazil, which ended in quarter-final defeat to the hosts.
But on Saturday, the 28-year-old made his comeback as the Ligue 1 runners-up drew 2-2 with their Spanish opponents in the pre-season tournament's curtain-raiser at Arsenal's Emirates Stadium.
Falcao entered the action in the 72nd minute, coming off the bench to replace Dimitar Berbatov.
Monaco were 2-1 down at that stage, having taken the lead through Ruben Vezo's own goal on the half-hour mark.
Another own goal levelled the scores, Ricardo Carvalho putting through his own net, before Paco Alcacer put Valencia in front for the first time after 69 minutes.
Leonardo Jardim introduced Falcao shortly afterwards, and Lucas Ocampos' strike 10 minutes from time ensured Monaco avoided defeat.
