Howard Beckett, the assistant general secretary who is standing for leadership of the union, posted the message after Border Force officials detained two men.
Police Scotland released the Indian nationals after crowds surrounded the van on Thursday.
Mr Beckett tweeted: “Priti Patel should be deported, not refugees. She can go along with anyone else who supports institutional racism.
“She is disgusting.”
He subsequently deleted the message and apologised.
He has now been suspended by the party, according to the PA news agency.
He later said: “Priti Patel message on Eid al Fitr is to deport Muslim refugees. Those who have been forced to flee war zones.
“We are seeing appalling institutional racism again and again from the supposed pillars of the British elite.
“Our society should have no place for racism, at all.
“I’m very sorry for my earlier tweet. I was angry to see Muslim Refugees being deported on the morning of Eid al Fitr.”
He said his earlier message was “never intended to be literal” and “the wording was wrong” and “offensive”.
“I apologise unreservedly to Priti Patel. No one should be deported.”
It is understood neither of the men involved in the situation in Glasgow is Muslim.
A Labour spokesman said the party “takes these allegations extremely seriously” and promised appropriate action.