In the first crash on Tuesday afternoon, officers approached a stationary car with a smashed windscreen in central Bourke Street and found a man slumped at the wheel with blood on his forehead.
"The person woke up, started the car and then reversed into a police vehicle and tried to manoeuvre its way out of that particular spot," Deputy Commissioner Andrew Crisp told reporters on Wednesday.
"The person was tasered and subsequently arrested and has been charged with conduct endangering life."
Bourke Street was a scene of carnage in January when six people were killed and dozens injured after a car drove through the busy city precinct, mowing down pedestrians.
Mr Crisp says he doesn't believe Tuesday's driver posed a real threat to other members of the public, but he allegedly had two guns in the car when arrested.
About 30 minutes earlier, a police car was rammed at Werribee, with the driver speeding off before being arrested.
The incidents come as the Victorian government on Wednesday introduced a bill to parliament making the ramming of emergency service vehicles and personnel a specific offence, complete with lengthy maximum jail times.
Intentionally driving at an emergency, custodial or youth justice worker would have a maximum jail term of 20 years while damaging an emergency vehicle will carry a five-year maximum.
Premier Daniel Andrews says the government continues to meet with police and ASIO regularly to review the policies.
"The Bourke Street incident earlier this year was a significant wake-up call for us, as a community, in terms of the use of vehicles as a weapon," he said.
Mr Crisp says ramming emergency vehicles is "dumb and just plain wrong".
"It has become a soft option for crooks to ram a police vehicle believing they will get away. To the credit of our members, in many cases that is not the case," he added.
The government also announced on Wednesday that permanent bollards to protect pedestrians in the Melbourne CBD will be be in place by Christmas, replacing temporary concrete blocks, and the city will have an emergency warning siren installed.
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