Barca trailed to first half goals from Kevin Gameiro and Daniel Parejo until Messi intervened, goal.com reported.
The Barca talisman scored from the spot five minutes after Parejo doubled Valencia's advantage and then leveled the proceedings in the 64th minute to earn his side a point at Camp Nou.
But Messi appeared to suffer with a thigh issue minutes after that second goal, receiving treatment on the touchline before returning to the action as Valencia held on.
The Argentine did finish the contest but there remains obvious concern for the Barca captain with a Copa del Rey Clasico against Real Madrid just four days away.
Valverde confirmed Messi had an issue, though he is uncertain its precise nature and will wait for answers ahead of tests before his deciding the star man's status for the Madrid contest.
"[Messi] has a small problem," Valverde said after the match. "I don't know exactly what he has.
"We will have to wait to see what medical staff say. If he's in good shape, he'll play on Wednesday [against Madrid]."
Meanwhile, midfielder Ivan Rakitic was impressed with the way Barca responded to the two-goal deficit, although he was left frustrated that they could only claim one point.
"We had a great desire to turn it around," Rakitic said. "In the second half, we were far superior. It was like we were playing handball. We were just missing a goal."
Barca and Real Madrid will play their first leg Copa del Rey clash at Camp Nou on Wednesday, with the second leg set for the Bernabeu on February 26.