Yes it is and carries a misdemeanor 4 penalty if caught and arrested. The Ohio Revised Code gives business owners the option of posting a sign like this if they don't want CCW on their premises. If arrested the likely charge is ORC 2911.21 (A, 4)
http://codes.ohio.gov/orc/2911.21
(A) No person, without privilege to do so, shall do any of the following:
(4) Being on the land or premises of another, negligently fail or refuse to leave upon being notified by signage posted in a conspicuous place or otherwise being notified to do so by the owner or occupant, or the agent or servant of either.
and ORC 2923.126 (c, 3, a):
http://codes.ohio.gov/orc/2923.126v1
(3)
(a) Except as provided in division (C)(3)(b) of this section, the owner or person in control of private land or premises, and a private person or entity leasing land or premises owned by the state, the United States, or a political subdivision of the state or the United States, may post a sign in a conspicuous location on that land or on those premises prohibiting persons from carrying firearms or concealed firearms on or onto that land or those premises. Except as otherwise provided in this division, a person who knowingly violates a posted prohibition of that nature is guilty of criminal trespass in violation of division (A)(4) of section 2911.21 of the Revised Code and is guilty of a misdemeanor of the fourth degree. If a person knowingly violates a posted prohibition of that nature and the posted land or premises primarily was a parking lot or other parking facility, the person is not guilty of criminal trespass in violation of division (A)(4) of section 2911.21 of the Revised Code and instead is subject only to a civil cause of action for trespass based on the violation.