Prof Katunguka said the university will reopen on October 17 for only finalists and this also applies to its two learning centres in Bushenyi and Soroti.
Mr Mbabazi had spent some time without appearing or speaking at public functions despite being seen at some state events.
The continent's hardest-hit nation, South Africa has reeled under one of the world's strictest lockdowns.
Party MPs, district chairpersons and members of the NEC will choose between Patrick Amuriat and Wasswa Biriggwa for the flag on October 6.
The Health ministry says those involved in the research are in the final stages of bringing the vaccine to Uganda for further trials