The motorway is shut between junction 3 and 4 this weekend, with drivers being diverted across the Hampshire countryside.
Hampshire's Constabulary's roads team have urged people to take note of road signs, after collisions near Romsey this morning.
The team tweeted: 'Please heed the road closure signs in and around the A3057 at Romsey. They are there for a reason.
'Already been two collisions on the rural roads and assisted this driver at Toothill. Be patient please and be safe!!'
The unit also posted a picture of a car which had fallen into a roadside ditch.
The M27 stretch is closed until Monday morning while Highways England carry out repairs on the Romsey Road bridge.
For drivers travelling westbound Highways England has put a diversion in place over nearly 60 miles, taking vehicles up the M3, A34 and back down to Southampton via Salisbury. Â