Falcao underwent surgery on his left knee in Porto on Saturday, three days after being hurt in Monaco's 3-0 Coupe de France win over fourth-tier outfit Monts d'Or Azergues.
The 27-year-old looks certain to miss the remainder of the season, and is also facing a race against time to feature in his country's FIFA World Cup campaign in Brazil.
Monts d'Or Azergues defender Ertek publicly apologised to Falcao on Friday, saying he felt "embarrassed" to have caused the former Atletico Madrid man's injury.
And Falcao took to his official Twitter profile to thank Ertek shortly after his operation, insisting the centre-back should not feel guilty as the incident was an "accident".
"Soner Ertek, thanks for your posts," wrote Falcao.
"Do not blame yourself, for what happened."
Falcao has scored nine goals in 17 Ligue 1 appearances this season, helping Monaco to second place in the table behind champions Paris Saint-Germain.
