Emergency crews arrived on scene on the A31 near Ringwood between Picket Post and Stoney Cross.
Traffic has been reported as solid with one lane blocked following the incident around 5.30pm.
Man dies after dog attack at Hillson Drive recreation ground in Fareham - owner is arrested
Fareham dog attack: Shrine set up in memory of man who died - named locally as Wiggy Symes
Heartfelt tributes paid to Wiggy Symes who died after Fareham dog attack
Fareham dog walker and trainer Ian 'Wiggy' Symes thought to be killed by XL American Bully breed dog
Thunderstorms yellow weather warning issued over Waterlooville, Fareham and parts of Hampshire by Met Office with chance of 'heavy rain'
Delays of up to 50 minutes has been reported by live travel service Romanse.
Traffic is also slow westbound past the scene, it has been reported.