In a statement to the Innovation, Universities, Science and Skills Select Committee, the BMA says there has been a "dramatic" decline in the subject's academic workforce in the past decade.
Since 2000, the number of senior academic trainees and fully qualified academics has fallen by per cent to 2,937, it says. This has coincided with an "unparalleled increase" in the number of medical students and medical schools.
"This means there is extra pressure on the remaining academics to deliver teaching to ever larger numbers of students on top of their clinical and research commitments," the BMA writes.
The submission to the select committee also reports that there is a growing reliance on non-medical staff to teach medical students.
And it says that the recruitment crisis has been compounded by the "relatively unattractive nature of academic posts", including the lower pay on offer compared with the salaries enjoyed by clinicians.
The BMA adds that the ageing workforce in medical schools "gives the impression that academic careers are not worth pursuing by younger generations of doctors".
Peter Dangerfield, co-chair of the BMA's Medical Academic Committee, said that a professorship was no longer considered the pinnacle of a medical career.
The length of time spent training to become an academic was offputting for many, as was the unnecessary isolation of academic work from clinical practice, he said.
"As a graduate doctor, I would want to have patients around me. I don't want to abandon my training," he added.
The BMA called on the Government to review the way medical research is funded and to set up programmes to give young people a taste of academic medicine and encourage them to consider it early in their careers.