With Monday's 106-102 home loss to the Denver Nuggets, the Clippers have now lost those three games Paul has been out.
Fellow starting guard J.J. Redickjoined Paul on the bench. Redick, who missed his first game of the season due to injury, is also nursing a sore left hamstring after sitting out the fourth quarter of the Clippers' Christmas Day loss to the Los Angeles Lakers.
Coach Doc Rivers didn't commit to a firm timetable for either guard's return.
"You never know. Again, we thought Chris was mild -- and it is -- but he's going to end up missing three games ... or, I don't know, two games," Rivers said before Monday's game. "I don't know how mild that is when you think about it. You just don't know with hamstrings.
"The one thing you do know, I think we've all learned over the years, is you have to be more cautious than if it was a sprained ankle. A sprained ankle you could still go out and play. With hamstrings, you just can't take a chance."
Paul suffered the injury in the third quarter of the Clippers' win over the San Antonio Spurs on Thursday. The last time the nine-time All-Star strained his left hamstring was during Game 7 of the 2015 first-round playoff series against the Spurs. Paul fought off the injury to sink the series-winning shot and send the Clippers to the second round that season, but sat out the first two games of the next round against the Houston Rockets.
The Clippers are increasingly short-handed. They're already without Blake Griffin, who is expected to miss four to six weeks after undergoing arthroscopic surgery on his right knee Tuesday.
The team is 1-7 without Griffin and Paul in the last two seasons.
The schedule isn't offering much relief, either. Monday night's game against Denver marked L.A.'s fourth game in five nights, which gives way to an upcoming stretch of five games in seven nights.
"The four-in-five nights is almost as bad as the injuries. But it is what it is," Rivers said.
Paul is averaging 17.6 points, 9.6 assists and 5.2 rebounds per game in 30 games this season. Redick is averaging 15.4 points and shooting44.9 percent from deep in 31 games this season. He missed one game earlier this season for rest.