There were reports saying Mbappe will have to go back to France to get his injury checked, but the youngster downplayed the concerns.
The 19-year old striker, who plays for Paris Saint-Germain, hurt his left ankle due to a tackle from defender Adil Rami and was unable to continue with the practice.
Mbappe was seen grimacing in pain and holding his left ankle.
"As long as I am on the field, I am happy", the Atletico Madrid forward said.
Allaying fears over the problem, Mbappe said via his official Twitter account: "I'm fine, it's just a knock so it doesn't matter but thanks for your messages".
That was just the attacker's second full senior season having broken into Monaco's first team as they won the title in 2016-17, Mbappe scoring 26 goals in all competitions as they also reached the Champions League semi-finals.
The teenager scored 21 goals in all competitions and also found the back of the net for France over the weekend as they drew 1-1 with U.S. in a warm-up match. "I hit the ball poorly and I fell - it is nothing serious".
The incident left Rami red-faced, with France opening up their World Cup campaign in Russian Federation on Saturday, when they play Australia at 11am BST.