The midfielder was forced off in the 80th minute of the Reds' 1-0 defeat to Atletico Madrid in the Champions League on Tuesday evening.
A stretcher was initially called for the skipper, but Henderson walked off the pitch unaided before heading down the tunnel for treatment.
Jurgen Klopp has now confirmed that Henderson, who underwent a scan on Friday, is facing a short stint on the sidelines.
"It could have been worse," Klopp told reporters on Friday.
"How we all know, it was a hamstring thing, and we've heard of different hamstring injuries around the Premier League - Harry Kane, for example - it's not that bad.
"But he will be out for, I think, three weeks or so, which is not cool. But, how we see it, we were still lucky."