The Barcelona midfielder believes his Argentine teammate must rest to recover from his latest injury to avoid it potentially ruining his season.
The 26-year-old went off midway through the first half of the Catalans' 4-1 win over Betis with a hamstring problem, in the process making it five Liga games without a goal for the Argentina international.
Fabregas, who is also set to undergo tests after complaining of discomfort in his knee, starred in his teammate's absence with two goals and does not believe that Messi should rush back into action.
"[Messi] has to stop to take the time that he needs to emphasize his explosiveness," the midfielder told Canal Plus on Sunday after the match. "Something similar happened to me and I was very screwed. You believe you're OK at first, but you're not. I was disappointed to miss out some games, but I know I'm at Barcelona and I will continue to grow.
"I spent the injury out of action, and even spent half a year with the ordeal which was not good, it was a very bad injury. Messi has to stop as it takes time to recover if it does not heal properly."
Fabregas also alleviated fears that the knock he picked up in the clash with Betis could see him sidelined for some time, though he acknowledged it has been hindering him since the Champions League win over AC Milan midweek.
"It will not be serious," the former Arsenal man added. "Just a minor annoyance. I had a major injury in the region not long ago, so I preferred to come off the pitch early. I was already not comfortable against Milan."