The midfielder went down off the ball less than 10 minutes into the Premier League clash at Stamford Bridge with the teams still tied at 0-0. The Chelsea medical staff quickly signalled he needed to be taken off and was replaced by Ruben Loftus-Cheek.
The France star's injury makes him a doubt for the Blues' remaining games of the season. Maurizio Sarri's side host Eintracht Frankfurt on Thursday looking to book their place in the Europa League final, having drawn 1-1 with the German side in the first leg.
Next week, they travel to Kante's former side as they end their Premier League campaign with an away game against Leicester City.
Speaking after the 3-0 victory over Watford, Sarri told reporters he is unsure of the extent of Kante's injury and feels he made a mistake in selecting him for the game.
“I don't know. The problem is with his hamstring. But I think that I made a mistake because, probably, today he needed to rest," he said in a press conference. "Sometimes it's very difficult to put on the bench a player so important like Hazard, like Kante, but you have to do it. Otherwise you risk, and I have to say that I made a mistake.
“I don't know [the injury's severity]. We have to wait until tomorrow morning, I think, but I think it's very difficult for him to recover for the next two matches.
"But we want to play in the final, so he's lucky. We have to try and recover him for the final in case [we get there]."
Kante has played a key role in the London team's campaign, having scored five goals and set up four in 51 appearances in all competitions.
The suspected hamstring problem is his second injury in recent weeks as the 28-year-old suffered a rib injury last month against Burnley, but he overcame fitness concerns to feature in the next games against Manchester United and Frankfurt.
Kante has been given a new role at Chelsea this season after the arrival of coach Sarri and midfielder Jorginho from Napoli. Kante has played in a more attacking role to accommodate the Italian and there has been some debate over the effectiveness of the change.
But Sarri is sticking to his idea and is confident his team's defensive troubles can be fixed, while Kante says he is happy with his new position.
"It is possible [to play Jorginho's role], but the manager decides," he said in February. "It’s fine, it’s fine. I like this [more advanced] position. Prefer it? It depends on the game, but I enjoy it. I’m with the manager, and I’m enjoying the way I’m playing now.
"It is a position I used to play when I was in France. I’m enjoying participating more in the offensive positions to change the game. I am enjoying it."