Lawrence Relph, 49, also suffered serious leg injuries after falling from the seating at the Tabac corner during Thursday practice. Another British spectator managed to cling on and was unhurt.
"We both wrote him a letter saying the obvious 'sorry to hear about your incident, get well soon', and also thanking him for his support because he is a massive fan of the team," 2009 champion Button told reporters.
"He came here to watch Formula One, and hasn't watched anything. He's been in hospital."
Hamilton, the 2008 champion, added: "We wouldn't be here without our fans. They mean a huge amount to me and the team. We're grateful for all the support we get."
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