The man, from the Sefton Park area of Liverpool, was arrested at 7pm and will be taken to a south London police station for questioning today.
Ms Nickell, 23, a former model, was assualted and stabbed on 15 July as she was walking on Wimbledon Common with her son Alex, who is three this week. He was found clinging to her body. Scotland Yard said last night that it was consulting Hampshire police about possible connections between Ms Nickell's attack and the murder of Katie Rackliff, a 19-year-old hair dresser.
Her half-naked body was found in June near a cemetery in Farnborough.
Evidence from both cases will be sent to Paul Brittan, a Home Office psychologist, who will look for similarities in the cases.