The round 4 match now will be played on a later date.
Ulster will return to action on September 28 when they face Cardiff Blues at the Arms Park.
A moment of silence will be observed at each of the other five PRO12 matches this weekend and Ravenhill is to host a memorial service on Sunday afternoon (3pm).
An Ulster Rugby statement read: “Further to the death of Ulster player Nevin Spence last weekend, the match between Zebre and Ulster due to be played on 21st September 2012 in Parma will be postponed to a later date.
“An announcement will be made in due course with the rescheduled match information.”
Among those reflecting on a young life cut down in its prime was Irish Tanaiste Eamon Gilmore who visited Ravenhill to pay his respects on behalf of the Dublin Government.
Mr Gilmore described the accident as a “deep, deep tragedy.”
“This was a huge tragedy for the family,” he said.
“I want to express my condolences to Mrs Spence, to the family, the two daughters.
“I grew up on a farm, I understand how something like this could happen. I can picture how it could happen.
“It's a deep tragedy, it's a great loss and I think that everybody on this island of Ireland will express their sympathy with the Spence family.”