The singer - who is widely known for lampooning other artists - pokes fun at Gaga's comparisons to Madonna by including a number of references to the Material Girl in his video for the single 'Perform This Way' including showing Yankovic's character attacking a cone bra-clad Madonna.
He also mocks Gaga's eccentric fashion sense by dressing as a variety of outrageous characters including an evil queen, a jelly bean and a troll and donning a unicorn headdress, porcupine hat and dresses made out of bubbles and knives.
However, despite reports Lady Gaga was unimpressed with his parody, Al revealed she "loves" the song so much, she gave him permission to feature it on his album 'Alpocalypse'.
He said on his blog: "Gaga loves the song. I'm thrilled on many levels to hear this because one, I truly respect and admire Gaga as an artist and it pained me to think of her as having less than a great sense of humour, and two, it means I get to put it on my album."