Davies and McHugh accidentally clashed heads during the second period of City's win over Port Vale, resulting in the pair both needing on-pitch assistance.
The defensive duo were both fine to continue the match, however, with McHugh going on to score the match-winner in injury time.
Parkinson confirmed: "They are both fine.
"At the time, it was a slight concern given that we didn't have another defender on the bench due to (Matthew) Batesy and Matty Taylor being injured. Thankfully though, both are fine and have trained this (Thursday) morning."
Matthew Bates (hip) and Matt Taylor (foot) will continue to miss out this Saturday, however.
Bates should be back in the next one-to-two weeks but Taylor is expected to be sidelined for longer after tearing a muscle in his right foot.
Italian winger Raffaele De Vita will also be ruled out for this weekend after another minor set-back with regards a recent hip/groin problem.
Parkinson explained: "Raffa is having an injection on his hip on Monday to try and finally clear up this problem he's got. We hope that it will do the trick.
"He has been doing some running out on the training pitch lately so we have been able to maintain his general fitness levels. He did have a full week of training (in the build up to the Crewe Alexandra fixture) but he still wasn't completely comfortable with his problem.
"As we say though, hopefully Monday will help to clear it up. Three or four days after the injection, he should be back in training."