The experienced international duo are struggling with knee and groin injuries respectively.
Shanklin picked up a knock in last weekend's win over Ulster and will now miss the four remaining Magners League games and the Amlin Challenge Cup tie with Newcastle.
"Tom won't really play a part for the rest of the season and I would say he is a doubt for the summer tour," said Blues coach Dai Young.
"The injury is not a huge worry - it is not the knee he has had problems with in the past - but he is going to need something done."
With the full extent of the injury still unclear and the best course of action with regards to recovery undecided, Shanklin may be forced to sit out Wales' summer series in New Zealand and their Millennium Stadium clash with South Africa.
More importantly for the Blues, they will not be able to count on his efforts as they look to secure Heineken Cup qualification by finishing among the top three Welsh regions.
Fellow 2005 Lions tourist Cooper was an unused replacement against Ulster last Friday but he too will miss the return trip on Saturday as well as the crucial league games against the Scarlets, Dragons and Munster.
"We have to deal with it and juggle the squad to make sure we stay fresh," added Young.
"But, just like it would be for any side, it is a blow for us."
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