B737-700
Flight Crew Air Transport Pilot (ATP); Flight Crew Instrument; Flight Crew Multiengine
Flight Crew Last 90 Days 180; Flight Crew Type 8000
Physiological - Other
Deviation / Discrepancy - Procedural Maintenance; Deviation / Discrepancy - Procedural Published Material / Policy; Flight Deck / Cabin / Aircraft Event Smoke / Fire / Fumes / Odor
Air Traffic Control Provided Assistance; Flight Crew Overcame Equipment Problem; Flight Crew Diverted; Flight Crew Requested ATC Assistance / Clarification; General Flight Cancelled / Delayed; General Maintenance Action
Human Factors
Halfway through our flight; our B-Flight Attendant asked to come into the flight deck and talk with us.  When she got to the flight deck she indicated that there was a very strong cleaning/bug spray smell in the aft galley.  And; our C-Flight Attendant was complaining of coughing and a hard time taking a deep breath because of the strong cleaning smell.  Our A-Flight Attendant didn't smell anything.  No passengers were indicating concern and; we didn't smell anything.  I informed the Flight Attendant (FA) if she was medically concerned we would patch through to medic so she could communicate her concern.  All the FAs indicated they were feeling OK and did not want to contact medic.  They just wanted someone to look at the aircraft in ZZZ2.  At that point I told her we would put the packs to high to help eliminate the strong cleaning odor.  We contacted Dispatch through ACARS to discuss the situation and see if there was an anti-microbial spray completed the night before.  Also; to inform Dispatch that they were not comfortable taking the aircraft on our next leg.  Dispatch wanted a patch through ARINC. We agreed on a patch to medic. During their discussion; Dispatch sent us an ACARS to divert to ZZZ1.  The First Officer (FO) notified ATC of our intention to divert. I notified the FAs and passengers of our intent; as well. As a precaution we accomplished the Smoke; Fire; or Fumes QRC and referenced QRH Smoke; Fire or Fumes Checklist in case the situation escalated.  Dispatch notified us the aircraft had been sprayed the night before. We communicated with our A-Flight Attendant on what to expect on landing; taxi; and at the gate.We kept in constant communication with the A-FA to constantly reassess our situation.  On our descent into ZZZ1; medic recommended the two Flight Attendants in question use the portable oxygen.  With that information I notified ATC.  We then accomplished all appropriate checklists and landed uneventfully.
B737 Captain reported a fumes event during cruise resulting in health issues for some flight attendants and an eventual diversion.