The Grandmufti issued a decree in Srinagar on Sunday, terming singing as un-Islamic.
"I have said that singing is not in accordance with Islamic teachings," Ahmad told media.
The cleric said he has advised the members of the rock band to "abandon" singing as it is against Islamic teachings and will not help them in playing any constructive role in the society.
"Society cannot be built or developed by doing un-Islamic acts like singing. I have advised these girls, and other Muslims as well, to stay within the limits of modesty as prescribed for them," he added.
The all-girls band, which came to limelight in late December last year after their performance at the annual 'Battle of the Bands' competition in Srinagar, had defied the convention by stepping into the male-dominated field of music.
The girls' band has received abusive and hate messages on their Facebook page for defying convention by choosing the field of music.
However, support has been pouring in from all corners on social networking sites for the band and Chief Minister Omar Abdullah has also backed them.
Omar came out in support of the girls on Saturday saying police will probe the threats.
"I hope these talented young girls will not let a handful of morons silence them," he said.