The 27-year-old turned his right ankle when landing awkwardly after competing for a high ball with Marseille defender Nicolas Nkoulou in Sunday night's game at the Stade Velodrome. He had earlier scored his side's equaliser in a match the Principality club went on to win 2-1.
"Along with James Rodriguez, Falcao has been called-up by his national team and must go, even if it's just for them to assess his injury," a Monaco spokesman told AFP. Monaco coach Claudio Ranieri said after Sunday's game that Falcao had "a badly inflamed ankle".
Colombia sit second in the South American qualifying competition for next year's FIFA World Cup in Brazil, three points behind leaders Argentina with a game in hand. They are due to host Ecuador in Barranquilla on Friday before travelling to take on Uruguay in Montevideo next Tuesday.