The experienced international duo, who both toured New Zealand with the Lions five years ago, 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 as he is expected to be sidelined for between six and eight weeks.
"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."
Shanklin will have the knee cleaned out and may be forced to sit out Wales' summer series in New Zealand and their Millennium Stadium clash with South Africa in what is a second serious blow in the last 12 months.
This time last year, Shanklin missed the Lions tour of South Africa despite having been named in the original squad after he required surgery on an injured shoulder.
Fellow Lion 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."