"We are trying to establish exactly what happened and I would appeal to anyone that may have witnessed the collision to contact police," he added.
The accident happened on the A538 Altrincham Road, between Wilmslow and Hale, Cheshire, at about 1020 GMT.
The footballer's red Ferrari was badly damaged in the crash, with the front edge of the vehicle completely demolished.
One of the wheels came off, ending up about 200 yards behind where the vehicle came to rest.
'Obviously shaken'
Onlooker Jody Lomax was driving behind Ronaldo when the crash happened.
"The Ferrari went straight into the wall, his front left-hand wheel came off and then Ronaldo got out of the car," he said.
"I was shocked. Anyway he was all right, he was walking - he was a bit shaken."
The player was unharmed and attended training on Thursday
Mr Lomax added: "Obviously I was stunned at seeing a Ferrari go in the wall and seeing Ronaldo.
"He was obviously shaken - who wouldn't be? - but it's a shame about the car as well."
Manchester United confirmed that Ronaldo was not hurt.
A club spokesman said: "He was involved in an incident this morning. No other cars were involved.
"He's fine and is training as normal with the team this morning."
Police said the Portuguese international gave a negative breath test to officers at the scene.
Ronaldo came on as a substitute when Manchester United lost at Derby County on Wednesday night and is due to play for the club against Chelsea on Sunday.
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