They said warrants were executed at Ashworth hospital and a private address in south Wales on Thursday.
"A 49-year-old woman has been arrested in south Wales on suspicion of preventing the burial of a body without lawful exercise and remains in police custody for questioning. Searches of both locations are ongoing," police said.
Brady and his partner, Myra Hindley, were responsible for the murders of five youngsters in the 1960s.
They lured children and teenagers to their deaths, with victims sexually tortured before being buried on Saddleworth Moor, above Manchester.
Pauline Reade, 16, disappeared on her way to a disco on July 12, 1963 and John Kilbride, 12, was snatched in November the same year.
Keith Bennett was abducted on June 16, 1964 after he left home to visit his grandmother; Lesley Ann Downey, 10, was lured away from a funfair on Boxing Day 1964; and Edward Evans, 17, was killed in October 1965.
Brady was given life at Chester Assizes in 1966 for the murders of John, Lesley Ann and Edward.
Hindley was convicted of killing Lesley Ann and Edward and shielding Brady after John's murder, and jailed for life.
In 1987, the pair finally admitted killing Keith and Pauline.
Both were taken back to Saddleworth Moor in 1987 to help police find the remains of the missing victims but only Pauline's body was found.
Keith's mother, Winnie Johnson, has made repeated calls for Brady to reveal the location of his grave.
Hindley died in jail in November 2002, aged 60.
Brady, 74, has spent the last 25 years at the high-security Ashworth Hospital in Merseyside.
He was due to go before a mental health tribunal in July but it was delayed after he suffered a seizure.
The tribunal was to consider Brady's application to be transferred to a Scottish prison and be allowed to die. He has been tube-fed since refusing food 12 years ago.
-AAP
