Midfielder Henderson went off early in Liverpool’s last 16 second leg clash at Bayern Munich on Wednesday which Klopp’s side won 3-1 to reach the quarter-finals of Europe’s elite club competition.
The 28-year-old has been named in the England squad for this month’s European Championship qualifiers.
“With Hendo we know now it’s serious enough to rule him out for the weekend. The international break will be long enough to bring him back,” Klopp told a news conference.
“It was a little one with the ankle. It was the best scan we could get, but still not good enough. Not good, but OK.”
Fellow midfielder Naby Keita faces a fitness test to be in contention for the clash at 19th-placed Fulham, having missed the trip to Bayern Munich.
“With Naby we have to see if he can train today (Friday). Checks were positive, but we have to see if it stays positive,” Klopp added.
Victory will lift title-chasing Liverpool into top spot with 76 points, two points above champions Manchester City who take on Swansea City on Saturday in the FA Cup quarter-finals.
Manchester City will have a game in hand, but Klopp pointed out that they could face a tough run-in.
They have games against third-placed Tottenham Hotspur and local rivals Manchester United in April.
“When Manchester City have a game in hand, it’s not that important. We just want to win our game at the weekend.
“Manchester City’s game in hand is against Manchester United and that’s not easy, but we need to think about winning our games only,” Klopp said.
“We haven’t struggled psychologically with them ahead of us or us ahead of them, it’s being really focused on the football game.