"Very sad to hear that David Robertson, who helped me reach my dream of racing in formula one, has passed away," McLaren driver Button, who no longer worked with the Robertson duo, said on Twitter.
The Finnish broadcaster MTV3 reported that Robertson had suffered from cancer of the larynx.
It emerged a week ago that Raikkonen, who switched from Lotus to Ferrari over the winter, was now working with former F1 driver Mark Blundell's management company MB Partners.
"I have known Kimi's management and advisors for a very long time," said Blundell, "and as such, we are working closely together on behalf of Kimi."
In other sad news, it has been confirmed that GP2 boss Igor Mazepa, who headed the 2013 title-winning Russian Time outfit, has died at the age of 40.
According to media reports, it is believed the Ukrainian died after a blood clot.