Officers were waiting for tactical teams to arrive to arrest the suspect when his vehicle began to drive away, Mr Manley said.
Image: Austin Police chief Brian Manley said the suspect detonated an explosive in his vehicle.
One of the SWAT team members shot at the vehicle and a second officer was injured in the explosion.
Police said the suspect - who has not been formally identified - suffered "significant injuries" in the bomb blast.
US president Donald Trump, who had earlier branded the Texas bomber a "sick individual", praised law enforcement officials.
The suspect was identified in the last 24 hours after shipping an explosive device from a FedEx store in the Texas capital, the Austin Statesman reported.
Police then used mobile phone technology to trace the suspect to the hotel, according to reports. »