Gascoigne flew out to the United States last week and was admitted to the Cottonwood rehabilitation centre for treatment for alcohol addiction.
However the 45-year-old former England international suffered a reaction when undergoing a detox programme and was taken to a hospital in Tucson where his condition could be monitored.
Mabbutt, who has talked to Gascoigne regularly in recent weeks, told Sky Sports News on Sunday morning: "The first part of the treatment was the detox and unfortunately Paul had a very bad reaction to the detox which meant that as a precaution he was moved from the clinic to a hospital where he was put in intensive care so that they could monitor him.
"But I spoke to his medical team here in the UK who spoke to Paul this morning. It's not a life-threatening situation and Paul is back on the road to recovery and hopefully soon he will be back into the clinic to continue his rehab.
"Over the years he has had a lot of support from the football family, but of course it could be a long road to recovery. Now Paul's asked for the help we can focus on getting through this."
The rehab centre had earlier refused to comment on Gascoigne's condition, while his former England team mate Gary Lineker tweeted at 1am on Sunday morning: "Gazza is struggling, Let's hope he can hang on in there. Others have generously offered to help."
And current England forward Wayne Rooney said of Gascoigne's plight: "He was a hero of mine growing up and it's sad for everyone to see and read about.
"My best wishes are with him and hopefully he can get himself out of this situation. I'm sure everyone, every England fan and every Paul Gascoigne fan, wishes him the best of luck."
Gascoigne earned 57 England caps, playing a starring role in their run to the semi-finals of the 1990 World Cup, and represented Newcastle, Tottenham, Lazio, Rangers, Middlesbrough and Everton at club level.