Falcao took a heavy knock to the head when he was caught in a sandwich between goalkeeper Yoan Cardinale and defender Paul Baysse on Wednesday.
The Colombian international had been chasing a bouncing ball which Cardinale punched clear from just inside his area.
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Falcao, 30, did not reappear for the second half and was later taken to a Monte Carlo hospital for scans on his head and chest.
A member of Monaco's medical staff told AFP that the scans had shown "no problems".
Falcao, who rose to fame at Atletico Madrid, may still miss this Saturday's Ligue 1 clash with Angers but should return to face Bayer Leverkusen in the Champions League on Tuesday.
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Even so, Monaco coach Leonardo Jardim was left fuming.
"In most places in Europe that's a red card," he said.
"Referees should make sure that in these kind of situations there is proper punishment. It was like a rugby tackle."
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