The widely anticipated move was confirmed in an official statement shortly after reports emerged that F1 teams had decided not to go ahead with a scheduled testing session at the circuit next week.
Bahrain Crown Prince HRH Prince Salman bin Hamad Al-Khalifa said: "At the present time the country's entire attention is focused on building a new national dialogue for Bahrain.
"Although (F1 rights holder) Bernie Ecclestone had graciously made clear that a decision on the race was entirely Bahrain's to make and was not yet required, we felt it was important for the country to focus on immediate issues of national interest and leave the hosting of Bahrain's Formula 1 race to a later date."
The 2011 season will now get underway with the Australian Grand Prix in Melbourne on March 27.
No date has been set for a possible rescheduling of the Bahrain race, which was first held in 2004 when Michael Schumacher won, later in the year.
Ecclestone, who has been in constant contact with organisers over the race's fate, gave his reaction.
The F1 chief said: "It is sad that Bahrain has had to withdraw from the race, we wish the whole nation well as they begin to heal their country.
"The hospitality and warmth of the people of Bahrain is a hallmark of the race there, as anyone who has been at a Bahrain Grand Prix will testify. We look forward to being back in Bahrain soon."
Prince Salman in his statement added: "After the events of the past week, our nation's priority is on overcoming tragedy, healing divisions and rediscovering the fabric that draws this country together; reminding the world of the very best that Bahrain is capable of as a nation once again united."
Circuit chairman Zayed Alzayani expressed the hope of restaging the race.
"Bahrain's Grand Prix is a time of celebration and hosting the race is a source of great pride for Bahrain and Bahrainis," he said.
"It is a showcase to the world and we look forward to welcoming the teams and drivers and everyone involved in Formula One back to Bahrain in the very near future.
"I hope that F1 and our friends around the world will understand our decision at this difficult time."
Monday's announcement follows the cancellation of last weekend's GP2 Series race in Bahrain after pro-democracy protests that have led to deadly clashes with police.
The unrest in the small Gulf state of Bahrain is part of a wave of protests that have rippled across North Africa and the Middle East since the revolt that ousted Tunisian president Zine El Abidine Ben Ali in January.
There had been unease in the pits over the staging of a race in a country in turmoil, with Red Bull's Mark Webber one of the drivers to voice his reservations.
"When you hear of people losing their lives, this is a tragedy," the Australian told the BBC.
"It's probably not the best time to go there for a sporting event. They have bigger things, bigger priorities."