Police Scotland said the vehicle failed to stop after striking three women and two men on Rose Street in Edinburgh shortly before 1am on Sunday.
It headed on to Lothian Road where it was involved in a crash with a vehicle.
The police said the were no further injuries and the five injured people are now in a stable condition in hospital.
A 36-year-old man has been arrested in connection with the incident.
It is understood it is not thought to be terror-related or otherwise targeted, or linked to a medical condition.
A Police Scotland spokesperson said: “Around 12.40am on Sunday, 12 September, we received reports of five pedestrians being hit by a vehicle on Rose Street near its junction with Frederick Street in Edinburgh.
“Two men aged 39 and 60-years old, and three women aged 37, 22 and 65, were taken to Edinburgh Royal Infirmary for treatment where they all remain in stable conditions.
“The vehicle did not stop at the scene and continued to Lothian Road where it was involved in a crash with another vehicle.
No further people were injured.
“Officers arrested a 36-year-old man in connection with the incident. Inquiries remain ongoing.”
Police sealed off several streets, including Lothian Road up to the West Approach Road junction and Frederick Street as the investigation continued.
With roads closed, a number of Lothian Bus services were diverted for a large part of Sunday.
They were unable to serve part of Lothian Road, and buses were re-routed via Shandwick Place, Morrison Link and West Approach Road both directions until further notice.
Services hit included 1, 10, 11, 16, 22, 24, 30, 34, 36, 47, and the 124.
Lothian Buses confirmed the diversions lifted around 2pm.
The road closure and police investigation also impacted on local businesses.
Frederick Street shoe shop, The Brogue Trader, said it was temporarily closed while road remained closed.