That length of absence would rule him out of Friday's Heineken Cup trip to Castres and the Welsh derby with the Scarlets at the Cardiff City Stadium on October 22.
But while Parks will miss the Round 6 clash with the Blues' national rivals, Gethin Jenkins is expected to be fit to return.
The Lions loosehead rolled his ankle last time out and will join Parks in sitting out the French adventure. Although Parks isn't due to return until the Round 7 tie at Aironi, Jenkins should still face the Scarlets.
"They both had scans yesterday and it's looking extremely unlikely that they will be available," said Blues director of coaching, Dai Young, referring to Friday's match with Castres.
"Gethin's probably nearer to a return than Dan. He rolled his ankle, it's nothing long-term. If he's not back for this week, I'm sure he will be next week.
"Dan's a little further away with a foot injury. He could be out for two weeks but he's walking about on it.
"We will know more with the results but we're not going to put any players at risk."
Parks will be replaced in the Blues starting line up by Ceri Sweeney, the man who wore the No10 shirt for the majority of last term and earned a nomination for the Magners League Player of the Year.
"Dan and Ceri get on really well and support each other. They both want to play and Ceri has never let us down," added Young.
"They are two different players and have different strengths and weaknesses. I'm sure Ceri will be eager to step up this week and keep the jersey."
The Blues are currently preparing for the second round of continental competition without Wales flanker Martyn Williams, with his game preparations disrupted by today's disciplinary hearing in Dublin following a charge of allegedly dropping his knee into Chris Paterson last weekend.
Williams will learn his fate sometime this afternoon, with the region hopeful he will not face a spell on the sidelines.
"We're pretty much planning without Martyn this week. We trained yesterday, have a team run on Thursday and that's pretty much it so we have crack on without him.
"We all know he's not a dirty player. He is recognised the world over as someone who plays fairly. I don't think anyone would accuse Martyn of wrong doing on a regular basis."
In some good news for the Blues and for Wales, Tom Shanklin has recovered from a bang to the head and is expected to feature alongside Casey Laulala in midfield.
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