And the scientific association has called for more information to be gathered on teachers' subject specialisms, qualifications and drop-out rates, after conducting a review of workforce figures.
The Royal Society report points to high drop-out rates of nearly 16 per cent in science teacher training. And last year, recruitment of trainees also fell 10 per cent short of government targets.
Maths was the only subject with worse figures, which had a drop-out rate of 18 per cent and missed its recruitment targets by a similar proportion.
The report also says that some schools only advertise for general science teachers because they think they will not find specialists.
Michael Reiss, director of education at the Royal Society, said: "The Government talks about placing a great deal of emphasis on the importance of science and mathematics. It's time that people woke up to the true scale of the problem and did something about it."
Hilary Leevers, from the Campaign for Science and Engineering in the UK, said that the Government was basing its recruitment targets on flimsy and inaccurate workforce data.
But the Department for Children, Schools and Families rejected the Royal Society's criticisms and said that it kept track of a range of factors to ensure sufficient teachers were available.
A department spokesman said: "The Government has done a great deal to recruit more high-quality science graduates into teaching.
"We have set targets for improving the proportion of physics and chemistry specialist teachers, and our strategy of recruitment, retraining and retention is working."