Fire crews were called to the Hazelwood Bar in Darnley, south west Glasgow, at around 2.30am on Saturday.
No one was injured but the blaze caused "substantial damage" to the premises at 380 Nitshill Road, Police Scotland said.
They have launched an appeal for information after investigators said the fire was set deliberately.
Detective Inspector Tom McKean said: "Thankfully no one was injured as a result of this wilful fire but it is vital that we trace those responsible as soon as possible.
"I would like to appeal to anyone who was around the Nitshill Road area of Darnley in the early hours of Saturday morning and who has seen or heard anything suspicious to get in touch with us.
"I would also ask anyone who can give us information on who was responsible for setting this fire or the reason why the Hazelwood Bar was targeted to contact police as soon as possible."
Anyone with information is asked to call police on 101 or Crimestoppers on 0800 555 111.