The British Pakistani Christian Association (BPCA) said words "cannot express the insanity, the depravity of this situation".
Nabeel Masih, 16, is accused of blasphemy charges for clicking the like button under an image of the Kaaba in Mecca, one of the holiest sites in Islam.
A Muslim alerted officers to the post saying he found it insulting to his religion, police said.
The teenager has been held in custody ahead of a trial. If found guilty, he could face the death penalty.
BPCA chairman Wilson Chowdhry said: "If this kind of thing is sanctioned by the government - and by not interfering swiftly to put an end to it, they will in effect be sanctioning it - then the Pakistani government has taken leave of all moral sense, and any semblance or pretence of protection for its Christian and minority citizens.
"Pakistan already has the shame of officially being the 6th worst country in the world for abusive treatment of its Christians, only a hairs-breadth behind Syria, where Isis is massacring and raping Christians en masse.
"The precedent set by allowing this farce, this abomination to continue a second more will confirm that the insane are in charge of the asylum, that for all its protestations of promoting human rights, the deeds show that the Pakistani state is in bed with the worst of extremists."
Pakistan's blasphemy laws mean anyone accused of insulting Islam can be sentenced to death. The laws are often used by Muslims to settle personal scores.
Asia Bibi is one of the most high profile victims of the law. The Christian mother was sentenced to death in 2010 for allegedly insulting the Prophet Mohammed during a discussion with Muslim women.
She is exploring her final appeal option before she is put to death.
