The woman was sexually assaulted and strangled in September 1977 not far from her home in the southern German town of Roth. Despite offering a substantial reward and investigating 2,000 potential suspects, police were unable to solve the grisly crime until the case was reopened in April 2008.
It emerged that the suspect's DNA - which he had given in connection with another enquiry - matched traces found on the victim's clothing. The man was taken into police custody on December 29.
"The 76-year-old from Roth is now being held in custody. He has refused to talk about the crime," police said in a statement.