The 50-year-old Festerling's candidature was announced by Pegida leader Lutz Bachmann at a rally in the state capital of Saxony on Monday evening, Die Welt reported.
Bachmann called on his supporters to produce the necessary 240 signatures to confirm her candidature with the state authorities on Wednesday.
Festerling was previously a candidate for the Alternative for Germany (AfD) another right wing political party which has had considerable success in state elections in the east of the country.
But she was forced to quit the party after she praised “Hooligans against Salafists” a violent far right movement which claims to defend Germany against radical Islam.
Pegida marches regularly through Dresden to protest against 'the Islamization of the West.' Festerling's candidature will be its first foray into official politics.
While numbers of participants have been falling since the group's high-water mark in January, when 25,000 followers went onto the streets, Monday's rally saw an improved turnout of 7,100, up from 2,900 in the previous week.
Next Monday the Dutch far-right politician Geert Wilders will speak at a Pegida rally in Dresden.