Giovanni Lewis, 28, was left outside Heartlands Hospital at about 19:45 BST on 18 October.
A post-mortem found he died from a stab wound to the heart.
West Midlands Police said a 27-year-old man from Shard End who was arrested on Wednesday on suspicion of murder had been bailed pending further inquiries.
Mr Lewis's wife said her heart had been "ripped apart".
"Words cannot express how I feel right now, I do not know how I'm going to get through this, he was my soulmate," she said.
The wife of a man who was driven to hospital in Birmingham with a fatal stab wound has paid tribute to her "gentle giant".