Srnicek, 47, played for the English Premier League club between 1991 and 1998, returning for a short second spell in 2006-7.
"I can confirm that Pavel has suffered a cardiac arrest whilst running and is in critical condition in hospital," his agent Steve Wraith wrote on Twitter on Monday.
"Pavel was running last night and his heart stopped. He was like that for 20 minutes and was then rushed to hospital.
"He is in an induced coma until Wednesday. Then they will see if his heart is stronger and if so bring him out of the coma... no one knows if his brain has been too starved of oxygen."
Tomas Oborny, a spokesman for the Ostrava-Poruba hospital, said in a statement that Srnicek "is... in our hospital, but on the wishes of the family [we] will not disclose details."
The former goalkeeper was in England last week to launch his autobiography, "Pavel is a Geordie", before returning to the Czech Republic for Christmas.
He helped Newcastle win promotion to the Premier League in 1992-93 as part of the team managed by Kevin Keegan.
He also made 49 appearances for his country, whom he represented at the European Championship in 2000.
Srnicek's former club tweeted a message of support in which they sent their best wishes and said: "Get well soon, Pav."
The goalkeeper also played for Sheffield Wednesday, Portsmouth and West Ham in England, as well as spending spells in Italy, Portugal and with Czech club Banik Ostrava.