Henderson sustained the problem in Liverpool's UEFA Champions League Round of 16 first-leg defeat to Atletico Madrid in midweek.
However, rather than ruling the England international out of the run-in as Liverpool looks to secure its first Premier League title and a second consecutive European crown, the relatively mild issue should see a return in mid-March.
Henderson, who is considered to be among the contenders to be named PFA Player of the Year, appears set to miss the second leg against Atletico at Anfield on 12 March (AEDT).
The Reds have favourable-looking league fixtures coming up against West Ham United, on Tuesday (AEDT), Watford and Bournemouth, although they also play Chelsea in the FA Cup and visit Merseyside rival Everton immediately after the Atletico game. Henderson could well return for the derby.
"It could have been worse. We all know it was a hamstring thing," Klopp said.
"There are a lot of different hamstring injuries around in the Premier League - Harry Kane, for example, stuff like that. It's not that bad.
"He will be out for three weeks or so, which is not cool. But how we see it is that we're lucky."
While Henderson's absence is a significant setback, Klopp feels Liverpool is well-stocked in midfield, although Xherdan Shaqiri is "not close to team training".
"Hopefully nothing else happens," the manager added. "Hendo is exceptionally important, not only football-wise but for some other reasons as well that hopefully everybody knows.
"Yes, we still have options there. That's good. There's a chance for all of them, but there would have been a chance anyway. Hendo would not have played all the games from now until the end of the season.
"It's a position where we can react, so we will react."
Liverpool has a 22-point lead at the top of the league with just 12 games remaining, but Klopp suggested he was not looking to rest players against West Ham in order to prevent further injuries.
"I could [make changes] because, apart from Hendo, all the other boys are fit," he said. "But Tuesday to Monday, there is absolutely no need to do it. That's longer than we usually have.
"We will see who will start and stuff like this, maybe there will be changes, but not because of the Atletico game."