Detectives are investigating fires at the former Kaituna Bowling Club clubrooms in Serpentine Ave and the Bakers Dozen bakery in Mailer St.
The Fire Service was called to the former bowling club just before 2am on Saturday.
The fire gutted the concrete block building, shattered glass in windows and melted aluminium window frames.
Detective Sergeant Brett Roberts said it was first noticed by people driving past.
Police were keen to hear from anyone driving past the building, on the corner of Serpentine Ave and Maori Rd, between midnight and 2.30am.
"In particular, some voices were heard at 1am after it appears a car travelling down Serpentine Ave towards Princes St lost control, and possibly hit the concrete median strip at the intersection."
Another vehicle passing shortly after had stopped and checked on the occupants.
A scene examination by the Fire Service and the CIB indicated the fire had been deliberately lit.
"This was just a senseless act of arson," Det Sgt Roberts said.
"The building involved has been used as a resource for a community-based group, and is probably irreparable."
Dunedin City Council community and recreation services manager Mick Reece said the land was owned by the council, and leased to the Malcam Charitable Trust.
The trust used the building for part of its work training programmes.
Chief executive Rosie McConnon said the fire was disappointing.
The trust had lost some equipment, but had plenty of other facilities where those who had used the building could work instead.
In the second incident, people driving in Mailer St at 1.35am yesterday noticed smoke coming from the Bakers Dozen bakery and called the Fire Service.
The fire was discovered and attended to early and caused only slight damage, but because of the nature of the business, the clean-up involved was extensive, Det Sgt Roberts said.
Had the fire in the bakery, which is at one end of the Mornington shopping complex, gone undetected, it could have spread to quite a few shops, Det Sgt Roberts said.
The scene was examined by police and the Fire Service, who both concluded the fire was set deliberately and that there had also been a burglary.
Police would like to hear from anyone who was in the area between 11pm on Saturday and 1.35am yesterday and about any suspicious activity they might have seen.
