The Spurs midfielder hobbled off during the second half of his side’s 2-1 win over Norwich following a challenge from Todd Cantwell and he will be fully assessed once the problem has settled down.
Mourinho was initially too worried to ask his medical staff the severity of the injury immediately after the game, but offered a positive update when he left the stadium.
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He said: “It is not a crazy one – hopefully weeks and not months.”
He had earlier said in his press conference: “I prefer not to know before I come in here so I come with a normal face.
“I don’t want to come in here with a very upset face, so I’m even afraid to ask, but when I leave here I have to ask.”
While Winks is the latest injury victim, Spurs did at least welcome back another as skipper Hugo Lloris was given a surprise start.
Mourinho said only last Friday that he would be out until early February, but he replaced Paulo Gazzaniga in between the sticks.
Mourinho had mixed emotions, having dropped Gazzaniga on the back of keeping a clean sheet and saving a penalty at Watford on Saturday.
“It’s happiness to see one of the best goalkeepers in the world to be back,” he said.
“It’s a very good feeling for us but at the same time it is one of these decisions that sometimes we must have it, but it hurts. To leave Paulo out hurts.
“The good thing is that he is such a good member of the family and he is such a special friend of Hugo that I think he also shared our happiness to have Hugo back as a friend.
“For me he gave me a lot of thinking and I had to try to be cold to make a decision without emotions because to leave Paulo out is not easy.”
This was not pretty for Spurs, who even though they closed the gap on fourth-placed Chelsea to six points, they looked a side far from capable of qualifying for the Champions League.
Harry Winks was forced off injured last night (PA)
Having led in a promising first-half performance through Dele Alli’s 38th-minute tap-in, Norwich were in the ascendancy after Teemu Pukki’s penalty levelled matters.
But Son Heung-min’s 79th-minute header against the run of play gave Spurs their first win of 2020.
It left Norwich boss Daniel Farke accepting his side need a miracle to stay up as they sit six points from safety.
The German said: “We all believe, otherwise we would have raised the white flag. If someone can help working on this miracle then it is me with the lads.
“Miracles can’t just happen, you have to create them, you have to work it and our lads showed they are willing to work.”
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