The England international has been in fine form for the Reds this year, playing a key role in the team's midfield again after deputising at left-back last season, and will be missed on the final day of Premier League action.
As quoted by Ben Dinnery of ESPN FC, Klopp said: "It’s a little injury. It’s serious enough to put him out for today; he couldn’t train the whole week."
Klopp will of course be taking extra precautions over Milner with the Champions League final against Real Madrid just around the corner.
Milner has been absolutely instrumental in the competition, registering the most assists in a single campaign out of any other player since its inception.
The 32-year-old hasn't travelled with the squad for the Brighton game, and youngster Dominic Solanke is his replacement - the home with lining up with Solanke up top alongside Roberto Firmino, or with the Brazilian playing just off him with Mo Salah and Sadio Mane as the wide men.
Jordan Henderson returns to the side alongside Georginio Wijnaldum as a central midfield pairing. Just one point will guarantee Liverpool the top four finish they desire.