Formula 1 boss Bernie Ecclestone told BBC Sport that the decision whether to hold the race on 13 March would be down to the Gulf state's crown prince.Webber said: "When you hear of people losing their lives, this is a tragedy.
"It's probably not the best time to go there for a sporting event. They have bigger things, bigger priorities."
Protestors have re-occupied a square in the centre of Bahrain's capital Manama following the decision of the crown prince, Sheikh Salman bin Hamad al-Khalifah, to withdraw security forces.
In the early hours of Thursday, six people were killed as police cleared Pearl Square, firing live rounds at protestors.
The crown prince, who established the grand prix, has been charged with holding talks with opposition groups over reform in the country.
Opposition figures have said they want political reforms that will lead to a constitutional monarchy.
Some protesters have also called on King Hamad bin Isa al-Khalifah, the crown prince's father, to step down.
Webber, who finished third in the drivers' championship in 2010 after leading it for much of the season, is the first major F1 figure to voice concerns about whether it would be right to race in Bahrain in the circumstances.
The Australian, 35, added: "In the end the right decisions will be made. Maybe it is still the first race, maybe Melbourne is the first race, we don't know.
"It's not a big deal to be honest because there are more things than Formula 1 in Bahrain.
"They have bigger things, bigger priorities and that is what they want to work on over there, generations of issues.
"That's the most important thing for them to sort out and not to worry about Formula 1."
Earlier on Sunday, Ecclestone told BBC Sport he felt the crown prince was the right man to make the decision about whether to hold the race.
"He will decide whether it's safe for us to be there," Ecclestone said.
"I've no idea. I'm not there, so I don't know.
"We won't advise people to go unless it's safe."
The 80-year-old said a decision about the event would be made on Tuesday.
Complicating the issue is that the final pre-season test is scheduled to be held at Bahrain's Sakhir track a week before the first race, from 3-6 March.
That would mean many F1 team members being in the country for more than two weeks at a time when the situation is changing by the day.
Teams have already discussed contingency plans amid widespread expectation that the Bahrain test will be cancelled and moved to either Barcelona's Circuit de Catalunya, Jerez in south-west Spain or the Portimao track on the Portuguese Algarve.
Source: BBC Sports
