"The enemies would like to see us split and thrown to the four winds, and if you are harmed, then the whole nation would be affected," the scholars said in the fatwa.
"From a sharia [Islamic law] standpoint, you must not travel abroad."
Senior Sudanese officials have released statements in recent days raising questions over the wisdom of the trip, prompting speculation that they were planning to send another representative instead.
Before the authority issued its statement, Mahjoub Fadul, the Sudanese presidential spokesman, told the Reuters news agency security arrangements had been put in place in case al-Bashir did make the journey.
Qatar is not a member of the ICC and would have no legal obligation to arrest al-Bashir if he entered its territory.
Amr Mussa, the Arab League secretary-general, said last week that the 22-nation group would not act on the arrest warrant.
But Luis Moreno-Ocampo, the ICC chief prosecutor, has warned in the past that any aeroplane carrying al-Bashir in international airspace could be intercepted, though the court has no enforcement apparatus of its own.
International experts say at least 200,000 people have been killed in Darfur and more than 2.7 million driven from their homes in almost six years of fighting.
Khartoum disputes the figures and says 10,000 people have died.
The conflict began when rebels took up arms against the government saying their region was being marginalised.