The six-year-old daughter of Danehill Dancer gave birth to a bay colt at Coolmore on Saturday.
The stud reported the foal is “a handsome colt with a good head, a white blaze and great presence”.
The news has been greeted with great delight at his owner-breeder Khalid Abdullah’s Banstead Manor Stud in Newmarket, where Frankel stands.
Juddmonte Farms general manager Philip Mitchell said: “From the reports that I have received, Frankel’s first foal is everything we could have hoped for. These are very exciting times for everyone who has supported the horse and we much look forward to the rest of his first crop of foals.”
Chrysanthemum, who spent her racing days with trainer David Wachman in County Tipperary, was the first mare scanned in foal to Frankel last year, and this is her first foal.
Frankel, trained by the late Henry Cecil, retired from the track in October 2012 after taking his 100% record to 16 with victory in the Qipco Champion Stakes.
Frankel mated with 133 mares between February and June in 2013 at £125,000 (€150,000) a time.
The coverings yielded around £15 million (€18m), with his potential stud earnings estimated at £100m (€120.3m) plus.