Grovehill Road was closed both ways from Cherry Tree Lane to Coltman Avenue at around 4.30pm on Thursday, November 21.
Emergency services were at the scene, including paramedics and police, and drivers were urged to avoid the area.
One woman said she drove past and saw the "really bad crash".
Humberside Police said they had arrested a man on suspicion of a number of driving offences and money laundering.
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Scene all cleared
Our reporter on Grovehill Road has said the scene has been cleared and the road is now open.
Man arrested for drink driving and money laundering after fleeing crash scene
Humberside Police have issued the following statement.
“A man has been arrested following a collision on Grovehill Road in Beverley at 2.45pm today (Thursday 21 November).
“A black BMW collided with a parked car causing one to come to rest on top of a Vauxhall Corsa. No one has reported any injuries and the driver of the BMW fled the scene.
“Officers were quickly in the area and tracked down a man near Beckside thought to be involved. He has been arrested on suspicion of a number of driving offences, including driving while under the influence of drink or drugs and for money laundering offences.
“Emergency services remain on the scene until all vehicles can be safely recovered. Drivers are advised to avoid the area as there will likely to be travel disruption.
“Anyone with information that would assist with our investigation please call us on our non-emergency number 101 quoting log 303 21/11/19.”
'Really bad crash'
One woman said: “Really bad crash on Grovehill Road near the bike shop. That bend is really bad. Hope you’re all ok.”
Road closed in both directions
Traffic system Inrix says: “Grovehill Road in both directions closed due to accident from Cherry Tree Lane to Coltman Avenue.”