Alderweireld sustained an adductor injury in Saturday's win against Manchester City.
The centre-back is out of Thursday's Europa League tie against Bulgarian side Ludogorets and could miss several crucial Premier League matches as the leaders bid to cement their place at the top.
"He has a muscular injury but not as big as we initially thought," Mourinho said.
"He will have time to be out, but not like a month which was immediately what we thought. I would say between two and four weeks.
"It's bad news, he was playing his best football. He's an important player that we'll miss."
There had been doubts over the match taking place with reports in Bulgaria suggesting some of Ludogorets' players had tested positive for coronavirus.
But Mourinho said: "According to my information, that's not true.
"Of the team that comes (on Thursday), I believe only two players who played against us are not playing. Apart from that, the other nine are in the list and ready to play.
"I don't understand the news, there is a big contradiction between the news and the information we have."
Tottenham's march to the top of the Premier League has come as a surprise to some after they failed to finish in the top four last term.
But winger Lucas Moura believes Mourinho's pedigree as a serial winner of silverware gives them a good chance of ending a trophy drought stretching back to 2008.
"Everybody knows Mourinho. He is a winner and he has won trophies at every club," Lucas said.
"I want to win with him and I think we deserve to win a trophy. In the last 10 years the club has done well - and it's time.
"Why not think to win the Premier League? We have the capacity to win. I know it's too early and there's a lot of games to play but in every game we need to think we are capable of winning the Premier League and that every game is important."
As well as his winning mentality, Mourinho has also brought a sense of fun to the Tottenham training ground.
The Portuguese boss had to fork out £500 ($669) on Spanish ham after losing a bet with left-back Sergio Reguilon after the weekend victory over Manchester City.
"I need to say thank you to him for the ham," Moura said. "I love ham. I was not aware of what he said to Sergio and I was very surprised to see the ham. I like it."