The actor was running on the treadmill at his gym in Malad on Friday when he collapsed.
He was seen in shows like 'Kkusum' and 'Pyaar Ka Dard Hai', passed away on Friday afternoon.
The actor was in good health and was busy working out when he suffered a heart attack, his colleagues said. Abir was in his 30s.
Sayantani Ghosh, who was to work with the actor in a Bengali film titled 'Sakkhat', said she had spoken to him over the phone at 1:15 p.m. on Friday.
"We were planning to go for a movie together, and around 3 p.m., I got a call about his death. He was quite healthy and that's what is more disturbing. It's truly shocking," she added.
Actress Smita Singh, who worked with Abir in 'Kkusum', was shocked when she first heard the news.
"It is true, he is no more. I am really shocked at the news. He was hardly 33 or 34 years old. He was working out in the gym and suddenly got a cardiac arrest," Smita, who knew Abir since 2001, said.
Abir had also been a part of shows like 'Hotel Kingston', 'Kumkum', 'Choti Maa', 'Badalte Rishton Ki Daastan' and 'Ghar Aaja Pardesi'.
A day before his death, Abir had taken to Twitter to mourn the sudden demise of acclaimed filmmaker Rituparno Ghosh, who also suffered a cardiac arrest. He was 49.
"Rituda may your soul RIP. I'm honoured to be touched by your genius in this life," Abir had tweeted.
He also features in one of Anurag Kashyap’s upcoming films.
Goswami had got married just a year back. Kashyap and Ronit Roy were among those who rushed to his residence on hearing the news.