Schumacher, whose older brother is the famous seven time world champion Michael, is instead moving into management, taking up a shareholding in the RSC Mucke Motorsport team.
Also hanging up his helmet late last year was Coulthard, the 41-year-old who raced in the German touring car series alongside Schumacher at Mercedes since 2010.
"I was surprised (about Ralf Schumacher's decision)," Coulthard told the Kolner Express newspaper, "because I thought he wanted to stay on for another year.
"But I know from personal experience how hard it is to compete against these DTM guys. For me it (retiring) was right, and I think also Ralf has realised that it is time to go."