"We were contacted at just after 6pm (Monday local time) following reports a car had been in collision with a number of pedestrians on Water Street," Merseyside Police said in a statementÂ
"The car stopped at the scene and a male has been detained."
Police say the suspect is white, British and from the Liverpool area and it is understood Counter Terrorism Policing North West are investigating.
Prime Minister Keir Starmer issued a statement condemning the attack.
"The scenes in Liverpool are appalling - my thoughts are with all those injured or affected," he said.
Liverpool Football Club said it would "continue to offer our full support to the emergency services and local authorities who are dealing with this incident".
Footage circulating online appeared to show the vehicle speed up as it veered into pedestrians on both sides of the crowded street.
Officers surrounded the car as witnesses attempted to stop the driver, who was eventually detained by police. A huge police cordon is in place on Water Street where emergency vehicles line the road.
Emergency services were quickly at the scene and several casualties were taken away by ambulances.
A number of police officers could be seen lining the junction of Castle Street and Water Street and firefighters were also on scene.
Emergency vehicles including ambulances were allowed out of the cordon to leave the area.
Harry Rashid, 48, was at the parade with his wife and two young daughters when he witnessed the collision.
"This grey people carrier just pulled up from the right and just rammed into all the people at the side of us," he said.
"It was extremely fast. Initially, we just heard the pop, pop, pop of people just being knocked off the bonnet of a car."
Another witness said he saw a car "speeding up" before hitting pedestrians.
Mike Maddra told the PA news agency the "car turned left, mounted pavement, come towards us and runs towards the buildings".
He said "we got out the way and it was speeding up".
Maddra said he thought he saw two people being hit and added, "it looked deliberate" and "it has just ruined the day really".
Liverpool sealed the title last month with four games to spare and ended the season with a 10-point lead over second-placed Arsenal.
They lifted the trophy after their 1-1 draw with Crystal Palace at Anfield on Sunday.
During the celebrations earlier on Monday, the players and staff waved to the crowd from an open-top bus with the words 'Ours. Again.' emblazoned on the side, as red flares were lit along the route.
with PA