The 53-year-old, who was also known as Nowab Miah, and owned the Marple Spice restaurant in Marple, Stockport, was taken to hospital in a critical condition but died on Sunday afternoon.
Police are continuing to question a 14-year-old boy arrested on suspicion of robbery.
The stolen silver Mercedes was found abandoned in Watson Street in nearby Denton on Monday evening. Attempts had been made to set it on fire.
In a statement, Mr Islam's family said: "Our family cannot begin to describe what losing our father has done to us.
"The fact he was just in the wrong place at the wrong time and was taken from us so early leaves us devastated beyond belief.
"Dad was everything you could ask for in a parent: a mentor, a role model - our best friend. We shared everything with him and there was nothing we couldn't tell him that he couldn't fix.
"He was extremely loyal and nothing came between him and his family. Our mum is overcome with grief. Dad was her life partner, her best friend and her rock.
"They were inseparable since the day they met and we don't think she will ever be able to move on from this tragedy.
"To our dad, family and the community was everything. He dedicated his time to helping others and he was loved and respected by everyone who knew him.
"He would give his time and support to anyone who needed it without question, his loss is going to be felt by everybody.
"We as a family have felt overwhelmed and truly humbled by the sheer volume of messages from people everywhere expressing their love and support. It just emphasises how truly special our dad was.
"It's going to take our family quite some time to come to terms with losing our father so suddenly and in such horrific circumstances. We would appreciate our privacy being respected at this time.
"Hold your family members just that little bit closer tonight, appreciate them that little bit more, because one day you never know when that will be your last time."
Anyone with information about the incident should call 0161 856 9821 or 0161 856 9790, quoting log number 2499 of 08/01/2021, or Crimestoppers anonymously on 0800 555111.