The drummer is believed to have walked out before the encore at the Heineken Music Hall.
The band, who confirmed their long-awaited reunion last year, had completed the main set and were expected to return for an encore of 'I Am the Resurrection'.
However, frontman Ian Brown later returned to the stage and told the crowd: "The drummer's gone home."
"I'm not joking, the drummer's gone home," Brown said, according to NME.
"Get all your aggro out on me, I can take it. What can I say, the drummer's a c**t."
An audience member explained: "After the song ended, the audience [was] still clapping and yelling and hoping the band gets back [on].
"The stage [was] empty, but then the crew walked on stage to get the back line down. Then everyone in the venue started booing and throwing beers."
The Stone Roses embarked on their first tour together in 16 years in Barcelona on Friday.
Reni was the first 'classic' Stone Roses member to quit the band in 1995, and was later replaced by Robbie Maddix until their break-up in 1996.
Watch fan footage of the incident below