Dembele went off in the first half of the 3-1 Champions League win over former club Borussia Dortmund on Wednesday due to a thigh injury.
The winger is due to have tests to determine the extent of the damage, but he is likely at least to miss Sunday's LaLiga showdown with Atletico Madrid.
Dembele has suffered three thigh problems in 2019 as part of a succession of injuries that have blighted his Barca career since moving from Dortmund in August 2017 for an initial €105million fee.
The 22-year-old, who has started only five matches in all competitions this season, has also had his professionalism called into question during a difficult time in Spain.
Suarez has now urged the player and medical staff to do their utmost to halt Dembele's problematic injury record.
"Dembele and the doctors have to try and find a solution to his injuries," Suarez said after the match, as quoted by Sport.
"[They have to find out] how he keeps getting injured after he has recovered. We hope he's back with us soon."
Suarez broke the deadlock at Camp Nou on Wednesday before setting up Lionel Messi for the second goal, and the Argentina star played in Antoine Griezmann - who came on for Dembele - to score the third.
Jadon Sancho pulled a goal back for Dortmund but Barca saw out a win that secured their place in the next round.
While he says his partnership with Messi has become easy after five years at the club, Suarez admitted they were eager to get Griezmann a goal to boost his confidence after a run of six appearances in all competitions without scoring.
"I've always said that spending time together, being with each other day to day, for so many years, playing games together makes the connection with Messi easy," Suarez said.
"You start [running] knowing that he's going to put the ball in front of you. We always look for the best option. It's normal that we find each other because we're the two main forwards."
He added: "As has happened with other team-mates, knowing [Griezmann] was struggling to score, when we were up we looked for him. Antoine did spectacularly: he had chances and he scored. It's important for his confidence."