The defender was substituted in the second half of Swansea's 1-1 Premier League draw with Crystal Palace on Sunday, with Monk revealing afterwards that Williams had felt unwell overnight and very nearly missed out.
The 29-year-old was even seen by some to have vomited on the pitch during the match.
And, with Wales set to face Iceland in an international friendly on Wednesday, Monk has requested that Coleman takes Swansea's recent busy schedule into account when selecting his starting XI.
"I will never stop a player playing for his country," he said. “Knowing Ash he will want to and he's his own man, but hopefully Wales will be clever.
"It's a friendly, it's not a qualifier or anything, and hopefully Chris can help out and do Ash a favour – not just for Swansea but for himself, because Ash does need that rest.
"Players will always want to play for their countries, of course they will, and managers of the countries will always want their best players, and Ash is one of their best players. But Chris has been there himself and it's up to them to communicate and do what's best for the player."
In addition, Monk revealed Pablo Hernandez was suffering with a tight hamstring, while Wilfried Bony had also been feeling unwell.