City Attorney Jeff Turnage says council members will take a final vote in 30 days.
The Commercial Dispatch in Columbus reports the ordinance was adopted Tuesday on a 4-2 vote.
The ordinance bans smoking in "all enclosed public places," including restaurants.
It would allow smoking in "age-restricted venues," such as bars, restaurants and other establishments which only allow people age 21 or older to enter. Smoking would also be allowed in "private clubs," which restrict access to the general public.
It would allow businesses with three or fewer employees to designate enclosed smoking rooms, inaccessible to the general public. It would exempt non-enclosed areas of public places, including open-air patios, porches or decks.