Meredith had been suffering with a chest infection last week - something that led him to miss the club's official photo-shoot on the Tuesday - but the Australian was cleared to play at the weekend against Swindon Town.
Unfortunately for City and Meredith though, the Australian defender was still feeling the effects of the virus during the Swindon game, leading to him being substituted a few minutes after the hour mark.
Following Meredith's troubles at the weekend, Parkinson admits City will need to look again at the left back's fitness ahead of his side's trip to stadiummk, with the City boss revealing he has a potential loan signing in mind as a possible replacement.
With Alan Sheehan set to be begin his three-match suspension following his Swindon red card, Frenchman Christopher Routis is likely to be handed his City league debut at centre half.
Parkinson said: "The slight problem we have is with Mez (James Meredith) and his chest infection.
Parkinson said: "The slight problem we have is with Mez (James Meredith) and his chest infection.
"The doctor assured me that he was fine for Saturday (vs Swindon Town) but he clearly wasn't. Mez is a tough lad, he doesn't complain or come off unless he ready needs to.
"Hindsight is a wonderful thing - and we know now we shouldn't have played him - but I don't think we were given all of the information we needed at the back end of last week.
"We have played him in the Swindon game and he has had a set-back.
"I am going to have a conversation with our doctor and James this (Monday) afternoon to make sure he is in a better physical state than Saturday and that he is able to play (against Milton Keynes Dons).
"If not, we are going to have to bring someone in on loan rather quickly.
"I do have someone in mind to bring in. Ideally, he is not quite up to speed just yet in terms of match fitness because he is coming back from injury, so we just need to make sure we get that call right in terms of which way to go."
While Meredith is doubtful for the Dons fixture, there is better news regarding Mark Yeates, however, after the Irish attacker's left shoulder popped out of place during Saturday's Swindon game.
Yeates was in at the club's training on Sunday to have the problem assessed before declaring himself for selection for the MK Dons game.
Parkinson added: "It was typical of Yeatesy really, he came off the pitch on Saturday with his shoulder popped out and he still wanted to go back on.
"He was asking the physio to put it back in on the side of the pitch so that he could play on.
"He came in on Sunday to get it checked out, he has trained part of the session today (Monday) and he wants to play in the game on Tuesday.
"That is great for me as a manager to see that. He could easily be in the treatment room but he has got himself out there and put his name up for selection.
"All we have to make sure is that if we do put him out there, there isn't the risk of him doing some long-term damage."