An Antwerp court convicted him of supplying explosives for a foiled 2018 bomb plot against a meeting outside Paris of Iran's exiled opposition.
The Belgian government has said the treaty is the only way to secure the release of aid worker Olivier Vandecasteele, who was detained in Iran in February.
The constitutional court ruled that the treaty was "suspended" pending a final ruling within the next three months.
"There is for the moment no longer any legal basis allowing this transfer," Francois Tulkens, a lawyer acting for the opposition group the National Council of Resistance of Iran, told AFP.
Protests in Iran continue - in pictures
The Assadi case sparked a furious reaction in Iran.
The Antwerp court ruled that he had masterminded the bomb plot under diplomatic cover as an envoy to Austria, and thus had no immunity in Belgium.
Tehran has demanded that Belgium recognise Assadi's diplomatic status and release him.
Iran's plots against foreign officials and dissidents — in pictures
Mr Vandecasteele, 41, began a hunger strike over the "inhuman" treatment by his captors in Iran, his family said last week, expressing worries about his failing health.
He is one of several western nationals detained in Iran, in what foreign-based activists have said is a bid to extract concessions. Most of them also hold Iranian passports.