Despite failing to pick up victory on their first outing of 2018, Barca - who welcomed club record signing Ousmane Dembele back to action in the second half - remain strong favourites to progress through in next week's return fixture.
Barca took the lead soon after, though, as Arnaiz got on the end of Gomes's low cross at the back post to fire across goal and into the net.
Celta looked the better team either side of the goal and continued to probe away, and they were deservedly level 31 minutes in when Sisto gathered the ball from a tight angle and hammered it home after Jasper Cillessen had initially helped it onto the bar.
A good save prevented Arnaiz from putting the La Liga pacesetters in front early in the second half, before then diverting Lucas Digne's low cross wide of the post.
Barcelona were beginning to create the better of the openings as Denis Suarez missed a glorious chance via a first-time shot and, two minutes later, Sergio Busquets curled one against the frame of the goal.
Some nice interplay in the final third allowed Emre Mor to get a shot away, ending right in the hands of Cillessen, and the same player then slotted wide from an even better position.
Shots from Ivan Rakitic and Jozabed Sanchez also missed the mark, but there was so nearly time for a winner as Sergi Roberto guided the ball against the post after being picked out by Semedo from the final chance of the match.
Celta Vigo (4-3-3): Alvarez; Mallo, Gomez, Fontas, Jonny (Roncaglia 82'); Wass (Mendez 68'), Lobotka, Sanchez; Aspas, Maxi Gonzalez, Sisto (Mor 67')
Barcelona (4-3-3): Cillessen; Semedo, Pique, Vermaelen, Digne; Paulinho (Rakitic 71'), Busquets, Gomes; Vidal (Roberto 72'), Arnaiz (Dembele 72'), D.Suarez