The authority expects to fill all its posts for the start of the new session in August but fears that natural turnover will leave it, and other councils, facing shortages.
Gordon Smith, head of performance and development, told the education committee: "This situation is mirrored across Scotland."
East Dunbartonshire estimates there will be a need for an extra teacher or part-time teacher in every primary following the initial cut from August of 1.5 hours in class contact time, a key part of the post-McCrone agreement.
The authority is redeploying teachers in its permanent supply pool and adding seven posts at a cost of more than pound;237,000. It is also contracting existing expressive arts teachers to fill in the extra time in primaries and providing permanent contracts for some of this year's probationers.
Even then, Mr Smith fears that the supply of available temporary teachers will evaporate over the course of the session, leaving many schools without cover.
But concerns that probationer teachers who complete their one-year induction in June could by "default" win a permanent post rather than by competitive selection have diminished after a recent agreement in the Scottish Negotiating Committee for Teachers.
East Dunbartonshire had been worried that probationers who were asked to undertake 14-day cover at the start of next session would be entitled to a permanent post because they had completed a full calendar year's service.