Officers believe the blaze outside B&Q on Skipton Road was stared deliberately at around 10pm yesterday (7 February).
They are appealing for witnesses or anyone with information about the incident to come forward.
The fire was contained to the skip, which was full of wood, and no other damage was reported.
Inspector Penny Taylor, of Harrogate Neighbourhood Policing Team, said: “Not only is deliberately setting fire to things illegal, it also puts lives at risk.
“Fires can spread extremely quickly and unpredictably, which can have dire consequences for those who light them and innocent members of the public.”
Officers have been investigating fires at nearby farm buildings, which they believe may also have been started on purpose and could be linked to last night’s incident.
Insp Taylor added: “We’re working very closely with North Yorkshire fire service, businesses, land owners and others to reduce their chances of being targeted and to catch the offenders before someone is seriously hurt.”
Anyone who has information that could help the investigation is urged to call North Yorkshire Police on 101, select option 2 and ask for Liz Rutter. You can also email PC Rutter on Liz.Rutter@northyorkshire.pnn.police.uk