Having already seen Frank Lampard and Gareth Barry sidelined by injury, England can ill afford to lose another midfielder but Hodgson has eased concerns about Parker.
There had been serious doubts about the 31-year-old's form heading into the Euros after he missed Tottenham's final four games with an Achilles injury.
However, when asked if he has any ongoing concerns about Parker's overall fitness, Hodgson said today: "No, not particularly, no more so than the obvious one that we were going to have, that when he came to join us having not played for Tottenham in the last two or three matches in the league.
"So that was obviously going to be a factor, but we also knew we had lots of training time and now in the two weeks we've been training he's taken part in every training session and he's also played 60 minutes already and he's available to play tomorrow [Saturday].
"So he'll be getting fitter by the day, as will Wayne Rooney, and we're quite happy that by the time we play France people will be in good physical shape."
The problems in England's midfield have seen Jordan Henderson called up from the standby list, and Hodgson remains confident in the options at his disposal.
"I'm satisfied with the group we've put together, I believe in the group," he said.
"I'm disappointed to have lost two senior players, but on the other hand it's a great opportunity for someone else.
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"The door that closes on you is a door that opens for someone else."
Asked about why Manchester United's Michael Carrick was not pursued more vigorously for a place in either the squad or on the original standby list, he said: "The contacts with Michael were actually conducted before I took the job.
"It was made clear to me that he wasn't a player who wanted to be considered, so quite frankly he wasn't a player I did consider.
"He's a player that I've always admired, of course, and, who knows, in the future if these type of injuries continue, he might have a very important part to play."
Looking ahead to the opening Group D match against France on June 11, Hodgson said he was optimistic that his team could bring an end to Les Bleus' good run.
France's 2-0 win over Serbia yesterday [Thursday] extended their unbeaten sequence to 20 games under coach Laurent Blanc, and Hodgson said: "England-France has always been a very important fixture.
"The French seem to think it will be the key match in the group, but you never know that until the group gets going.
"We're looking forward to it and we know it won't be easy.
"The French are on a fantastic unbeaten run, but all runs have got to end sometime and we hope we're the ones that will bring that run to an end."
Tomorrow's [Saturday] friendly against Belgium will be notable for its use of a Hawk-Eye goal-line system, and Hodgson said he welcomed the opportunity to explore a technology that has long been in demand.
"I don't think there are too many people who have objections to goal-line technology," he said.
"I side with all my colleagues on that one. It's an advance, and one which I hope will prove successful and at least banish some of the ghosts of the past."
Looking ahead to the game against a Belgium team boasting the talents of the Premier League-bound Eden Hazard, he added: "The Belgians are a very good team.
"This is Wembley, there's 90,000 people, so we have to accept that whatever team we play they are going to pull out all the stops to beat us."