The shrine, visit by hundreds of devotees each day, has been partially damaged in the fire, authorities in Kohlu district said.
Kohlu deputy commissioner Ejaz Haider said some unknown persons had entered the shrine on Saturday and set it afire.
“But because people of the area gathered quickly and put out the fire the shrine was saved but a big portion has been damaged,” Haider said.
Five suspects have been arrested in connection with the case, he added.
Towaq Ali Mast – popularly known as Mast Twakali – was born in 1828. He spread the message of love for the humanity through his poetry.
The Tehreek-e-Taliban Pakistan and other militant groups, which consider going to shrines as un-islamic, have in the past targeted them.