The play-off fixture - probably against Calvisano - takes place in Italy on May 29, four days after the Lions squad depart for New Zealand.
Cardiff must win to secure a place in next season's blue riband European event and join automatic Welsh qualifiers Neath-Swansea Ospreys, Newport Gwent Dragons and Llanelli Scarlets.
But they will face the task without three of their most influential players.
"Over the course of the past week, I have consulted with the chief executive of the British and Irish Lions, John Feehan, Blues director of coaching David Young and other colleagues," said Cardiff chief executive Robert Norster.
"Given the importance of the forthcoming match in Italy, we obviously had to consider the pros and cons of pursuing the possible availability of Gethin Jenkins, Tom Shanklin and Martyn Williams for that match.
"As the same time, we had to respect the great honour that has been achieved by the three players in their selection for the tour to New Zealand, and the importance of their own preparation period, both before the tour begins and in the lead-up to the first Test.
"As former Lions, David Young and myself had every sympathy for their aspirations once the tour is underway.
"We also recognise that it would be insensitive on our part to ask the players to make their own decision about their availability for the play-off match.
"Consequently, I can confirm that the Blues will not be making further enquiries about Gethin, Tom and Martyn being made available for the play-off match.
"They will join with the rest of the Lions squad in the middle of next month at their pre-tour training camp."