Shafiq's campaign headquarters in Cairo had already been attacked on Monday.
The latest attacks came after thousands of angry protesters across Egypt took to the streets on Saturday after ex-president Mubarak and his security chief were given life in prison over the deaths of protesters in 2011 but six police chiefs were acquitted.
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A group of protesters invaded the headquarters of Shafiq's campaign in Fayyoum south of Cairo before setting fire to the building, the security official said.
Premises in Hurghada on the Red Sea were pillaged and the windows smashed.
The official said the blaze in Fayyoum had been brought under control and calm had returned around the buildings in both towns.
Shafiq is to confront Islamic Brotherhood candidate Mohammed Mursi in a second round of voting June 16 and 17.
The former premier is detested by young pro-democracy activists who launched a revolt against Mubarak last year, accusing Shafiq of being a pawn of the military who have run the country since the fall of the ex-president and seeing him as a symbol of the former regime.
