The 31-year-old will remain with his club West Brom to have treatment on an Achilles problem and ligament damage to his left thumb.
Manager Chris Coleman has not yet decided whether to call up a replacement with the rest of the squad due to report for duty on Wednesday.
"Personally I am going to need treatment on a couple of injuries I've picked up in recent weeks and need to get over," Myhill told wba.co.uk.
"I've not trained for a while and I'm glad for the rest because it means I can do some work in the gym with the physios so the break has come at a good time for me.
"I was really struggling last week and I'm grateful to the medical staff for the help they've given me to get on the pitch."
Despite the upcoming friendly, focus remains on the future of Coleman, whose contract is due to expire after the match.
Press Association Sport understands discussions with the FAW over a new deal to take the current boss through to the end of the Euro 2016 qualifying campaign have been constructive.
It is understood Coleman has indicated to FAW chiefs he wants to take Wales forward, and they believe he represents a safe pair of hands.
However, any expected agreement is not likely to be forthcoming until later in the week.