Araujo left the pitch in the 67th minute after clashing with team-mate Gavi and was sent to hospital for further tests.
The win saw Barca tighten their grip on second place in La Liga by taking seven points clear of third-placed Sevilla.
Memphis Depay opened the scoring after brilliant skill from Ousmane Dembélé and Pierre-Emerick Aubameyang doubled Barcelona’s lead just before half-time – despite being heavily outplayed in the first half.
Shortly after the break, Aubameyang scored again following another Dembélé assist, but a misplaced pass from goalkeeper Marc-Andre ter Stegen then allowed Iago Aspas to pull one back for Celta.
Hopes of a comeback, however, were dashed soon after as Jeison Murillo was sent off for a challenge on Depay.
There was then a long break in play as Araujo was treated before being taken off the pitch in an ambulance and replaced by Clement Lenglet.
“Today we did things well. Maybe the first half was a bit complicated, but in the second it was much better,” Aubameyang said.
“It’s positive for us to keep fighting for this second place.”
Asked about Araujo’s condition after the game, Barcelona manager Xavi said the defender was “fine” and would remain in hospital overnight.
Barcelona have two more league games this season – against Getafe on Sunday and Villarreal next week.
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