The man was also being questioned over the abduction of a 17-year-old girl, said a Greater Manchester Police spokesman.
Ms McGrath, 27, was murdered in a frenzied knife attack as she arrived to collect her boyfriend from the pub in Bramhall, Stockport.
Her father Brian McGrath, 55, is a district judge in the family division in Bolton and Bury.
Early yesterday a man was arrested in Caernarfon, North Wales, in connection with the kidnapping of the 17-year-old girl in Stockport. The police spokesman said: "In connection with (Ms McGrath's) murder, a 27-year-old local man is in custody in Stockport suspected of this offence.
"He is also suspected of the abduction of a 17-year-old girl from Stockport who was taken to Caernarfon, where she escaped unharmed.
"The man was unknown to either of the girls before these two incidents."
It is understood the 17-year-old girl, whose identity police are keeping confidential, was abducted as she was driving to work in Cheadle, Stockport, on Saturday morning.
A police operation was mounted after she managed to flee from the car in which she was being held. - PA NewsReuse content