It is part of a near £750,000 cut to the authority's public health budget which also includes plans to scrap free swimming for over-50s at the council's four leisure centres.
The quit smoking schemes have been acknowledged as being as massive success. Nearly 120 pregnant women were supported to give up smoking in 2014/15 and in total more than 1,000 smokers were supported to stop lighting up in the same period.
But council bosses say they have no choice and claim the cuts have been forced upon them by having their own public health grant from the Government slashed.
The authority had planned to spend £562,000 on quit smoking guidance and programmes in the 2015/16 financial year.
But in a report due to go before the council's ruling cabinet on Thursday, proposals are revealed to slash £190,000 from that to absorb some of the cuts from Whitehall.