Barnsley, who defeated Chelsea in a dramatic sixth-round tie at Oakwell on Saturday when Kayode Odejayi scored the only goal of the game, will face the Bluebirds in an all-Championship last four meeting at Wembley.
The Tykes will be making their first appearance in the semi-finals since 1912 when they went on to win the competition.
It is also Cardiff's first semi-final appearance since their own famous cup victory of 1927.
The Welsh club overcame top-flight side Middlesbrough 2-0 in another sixth-round shock on Sunday.
Meanwhile, sole Premier League representatives Portsmouth have been paired with Championship high-flyers West Brom after overcoming Manchester United in the last round.
Pompey boss Harry Redknapp is aiming to take the south coast club to a first final since 1939, but in his way will be a Baggies side which accounted for League One side Bristol Rovers in the sixth round.
The two ties will be played on the weekend of April 5 and 6.