The singer had been due to perform with the man band at Copenhagen's Parken stadium but fell ill after eating lobster and had to be treated for dehydration.
Posting a picture of himself on his blog, he told fans: 'Thank you for your messages and love. I'm not completely out of the woods yet but feeling much better. Gutted for everyone involved with the tour. Feeling dreadful for letting the fans down. I'm so, so sorry. Here's me and my drip.'
And a source told The Sun the band are crossing their fingers Williams will be better in time for their Amsterdam gig on Tuesday.
'It hasn't been pretty. It's all down to a dodgy lobster he ate at a hotel,” the insider said.
'Jason and Mark wanted to go ahead and do it without him, so as not to let down the fans. But there was something to do with the insurance that stopped them. I think they would have had to pay back on the tickets if people there said they wanted to see Robbie and they'd done the gig without him. '