The doctors' union - which represents the so-called resident doctors who make up nearly half of the medical workforce - said the strike would start on Wednesday, the latest of a series of strikes this year over pay and working conditions.
"Tens of thousands of frontline doctors have come together to say 'no' to what is clearly too little, too late," BMA chair Jack Fletcher said in a statement, saying members had rejected the government's latest offer on working conditions.
He said the union was still willing to work to find a solution.
The strike will add to pressure on an already stretched healthcare service after NHS England warned last week that hospitals were facing a "worst-case scenario" from a surge in cases of a virulent strain of flu.
Streeting appealed to the doctors to go to work.
"There is no need for these strikes to go ahead this week, and it reveals the BMA's shocking disregard for patient safety," he said, adding that the strikes were "self-indulgent, irresponsible and dangerous".
Streeting told Sky News that the government was open to the doctors' union rescheduling the strikes to minimise the risk to patients caused by the flu wave.
Flu hospitalisations in England surged by more than 50 per cent in early December, reaching an average of 2660 patients a day - the highest level for this period.
Health leaders have said there was still no peak in sight.
Europe as a whole has been grappling with an unusually early and severe flu season, with health authorities warning of rising cases across the continent.
The BMA said 83 per cent of resident doctors, previously known as junior doctors, rejected the government's offer in an online survey with a 65 per cent turnout of its more than 50,000 members.
The offer made by the government last Wednesday did not include new pay terms, something the BMA has been campaigning for even before the Labour Party won last year's election.
Shortly after coming to power Streeting struck a deal with the doctors, offering them a 22 per cent pay rise - seven percentage points below the 29 per cent sought by the BMA.
The union has also been pushing for a better pay offer from the 5.4 per cent pay increase announced earlier this year, saying resident doctors were still suffering from years of pay erosion.
