McLaren doctor treated both Hamilton and Dennis at Valencia
But team doctor Aki Hintsa also had to administer painkillers to treat boss Ron Dennis' bad back, the website of the British broadcaster ITV reports on Wednesday.
Hamilton, meanwhile, said before leaving the port city that he is confident his health troubles will be resolved prior to the forthcoming Belgian grand prix, which is to be staged back-to-back with the subsequent race at Monza.
On Wednesday, F1 teams began testing at the latter high-speed Italian circuit, and McLaren managing director Martin Whitmarsh on Wednesday said the British driver is expected to be fit to drive later this week.
Heikki Kovalainen was in action at the wheel of the single MP4-23 on the first day.
"(Hamilton's) physical problems are unlikely to disturb his fitness programme and we expect him to make a full recovery for both the Monza test and next week's Belgian GP," Whitmarsh said.