Four police officers in the unmarked police car were taken to hospital for further assessment on Thursday afternoon.
The prime minister was not involved in the crash near Elizabeth Town.
Tasmanian police said initial inquiries indicated a Mitsubishi Triton collided with the rear of the police vehicle while attempting to merge.
Two Tasmanian police officers and two federal police officers were conscious when transported and had "non-life threatening injuries" after the car rolled down an embankment.
Mr Morrison said he was relieved the officers were taken to hospital, where they were receiving care.
"Our police do an amazing job in keeping us all safe. I am incredibly grateful to all the police who look after me and my family," he wrote on Facebook.
"We have all got to know each other over the years. They are selfless, professional and incredibly generous. I hope to hear further good news about their condition.
"Jen and I also send our thanks, love and best wishes to them and their families."
Family members have been notified and are being kept up to date about their condition.
The driver of the other vehicle was not injured.
"As is normal process for a crash involving police, the Tasmania Police Professional Standards Unit has been advised and will monitor the investigation," Tasmanian police said.
Australia Federal Police said the matter was not being treated as a security incident at this stage.
The event Mr Morrison was due to attend was cancelled.
Labor leader Anthony Albanese sent his best wishes to the police officers.
"They do a fantastic job and I wish all a speedy recovery."
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