The accident happened on the M62 westbound just before the exit slip road at junction 22 around 3.08am.
One passenger on the single decker coach was treated at Huddersfield Royal Infirmary for minor injuries.
The other nine passengers were uninjured.
The HGV driver was treated in hospital in Oldham for whiplash.
Diversions were put in place between junctions 22 and 24 while the vehicles were recovered.
The uninjured passengers were able to continue their journey after alternative transport was put on for them by police.
West Yorkshire Police are appealing for witnesses.