A couple were walking their pug and baby at Baysgarth Park in Barton-upon-Humber at around 5.50pm on Saturday when the attack took place.
The black Staffordshire bull terrier, which had white on its chest, ran over to the couple and knocked the woman and her baby to the floor.
It then attacked the pug, causing a cut to its eye.
When the man tried to intervene, the dog bit him on the hand.
Members of the public rushed to help the couple.
Humberside Police are appealing for those who helped and any other witnesses to get in touch by calling them on 101 and quoting reference number 16/75354/21.