A scan on Friday confirmed Neymar had damaged tendons in his right ankle in Thursday's 2-0 King's Cup last 16, second-leg win at Getafe, which sent Barca through to the quarter-finals 6-0 on aggregate, and club medical staff estimated he would be sidelined for three to four weeks.
"What a scare!" Neymar wrote on his Instagram account.
"When I fell I thought of a lot of bad things.
"I thought it could have been a serious injury, I thought about my plans for 2014.
"But Jesus, once again, was with me and it was just a scare. I wanted to thank all those that prayed for me. And don't worry. I will do everything right and will be back in no time."
The injury was the latest setback for the 21-year-old, who had not started a match since Christmas due to a lack of fitness and a stomach bug.
He will miss Sunday's La Liga game at Levante as well as this month's two-legged Cup quarter-final, also against the Valencia-based side.
Before they play City in Europe's elite club competition, Barca have La Liga matches against Malaga, Valencia, Sevilla and Rayo Vallecano and the club said he would definitely miss the Malaga and Valencia games.