Indeed, Raikkonen went on to win 20 career grands prix and the title for Ferrari in 2007.
But since he returned to Maranello for 2014, the now 34-year-old has struggled at the wheel of the F14-T car, also piloted by Fernando Alonso.
"Kimi has problems and they need to be resolved," Hakkinen told Hermes.
"At the moment Alonso is utterly dominating him -- the difference is not small," 45-year-old Hakkinen, the title winner in 1998 and 1999, added.
"There have been four races and I would have expected him to settle in by now. His car is not so catastrophically bad that he can't do anything about Alonso," he continued.
"Kimi needs to do something, and he needs to do it very soon."
Notoriously, Raikkonen is no fan of driving simulators, but Ferrari's new facility is state of the art and Hakkinen urged him to use the gap between China and Barcelona wisely.
"The simulator is a good tool," he said. "You can try out all sorts of setting changes.
"But I don't want to be giving Kimi advice, because I'm assuming that a world champion is already concentrated on solving his problems so that he can beat his teammate and deliver decent performances," said Hakkinen.