The 46-year-old added: "He was standing by the microphone and he had the guitar in his hand and he kept shaking his left hand as if there was something not quite right with it. He walked forward to the microphone and he was trying to grab the microphone with his left hand, and it was swinging from side-to-side.
"I thought at first there was something wrong with it and he was trying to keep it steady. He then took three or four steps backwards. Then he just collapsed on the stage backwards. There was no one there to catch him, he just fell into a clump. He was on his back for about two minutes before they brought the curtain down and then that was it."
Mr Fewins said Rea "looked brilliant" ahead of collapsing, and said he had been talking to the crowd and getting them to clap along to the songs.
"He looked fit, he looked well. He was changing guitars every song, and he just looked like someone who I have seen several times and was playing the best I have ever seen," he said.
He said the unfolding situation, which came half-way through a song, "looked incredibly serious" and came as a shock to the audience.
Mr Fewins said staff eventually declared it was the end of the show and asked people to leave the venue. As he came out of the theatre Mr Fewins saw an ambulance with its blue lights flashing pulling away.
One fan wrote on Twitter: "Chris Rea has just collapsed on stage at the New Theatre Oxford where I'm watching him. Fell backwards in a clump on the stage. Really doesn't look good. I'm quite upset."
Another added: "Feeling devastated. While watching one of my guitar heroes, Chris Rea, play tonight, he just collapsed about an hour into his set. Ambulance took him away. Please pray that he is okay."
A spokeswoman for South Central Ambulance Service said: "We were called at 9.30pm to attend to an incident in George Street in Oxford. We had an ambulance crew on scene and one patient has now been taken to hospital."