All the victims were strangled with their own headscarves
The governor of Khorasan province said the 39-year-old was being interrogated and more details of the arrest would be given later.
Iranian police have begun rounding up prostitutes in Mashhad - one of the country's holiest cities - after the latest victim was found at the weekend.
Like the other targets, she was strangled with her own headscarf and wrapped in her chador, or veil.
Religious motive
One popular theory is that religious extremists have taken the law into their own hands to rid Mashhad of prostitutes.
Brigadier-General Mohammad Baqer Qalibaf said that the suspect - a builder, married with three children - had been arrested in Mashhad after a two-day operation.
The bodies of the 19 victims have been discovered over the past year. Mr Qalibaf said that three of the murders were believed to have been carried out by other killers who have already been arrested.
The killings have been dubbed the "spider murders" in Mashhad by people who thought the killer used headscarves to ensnare the women in the same way that a spider uses a web to trap its victims.
Mr Qalibaf alleged that the suspect began the killings after his wife was approached by a man who mistook her for a prostitute.
Organised crime
But an MP, Ali Zafarzadeh, believes that a sophisticated network is behind the killings.
He said the murders were similar to the 1998 serial killings of intellectuals and political dissidents by rogue elements in the intelligence ministry.
The Iranian authorities have come under mounting pressure to solve the murders.
Ali Tajernia, a parliamentarian from Mashhad, has demanded the removal of "incompetent" officials in charge of the case.
"If these murders had taken place anywhere else in the world, officials investigating them would have been sacked," newspapers quoted Mr Tajernia as saying on Tuesday.
All forms of prostitution have been banned in Iran since the 1979 Islamic revolution, but it has become more common in recent years.