The Brazilian was shown a yellow card in the 64th minute after jumping into Atletico defender Juanfran during an aerial tussle.
Barcelona had been in dominant form during the first half after goals from Luis Suarez and Lionel Messi had given the visitors a 2-0 half-time lead.
Antoine Griezmann replied for Atletico just before the hour mark and Neymar then collected the caution which will rule him out of next week's return at Camp Nou.
Neymar went close twice in the final minutes, but could not find the target as Barcelona recorded a 2-1 first-leg victory.
The 24-year-old has now gone three games without scoring for Luis Enrique's side, and has just five goals in 16 La Liga appearances.
Neymar has a return of 24 and 22 league goals in his previous two campaigns, having scored nine times in his first season after signing from Santos.
He was on target in the Copa del Rey quarter-final victory over Real Sociedad, netting from the penalty spot in the first leg.