Gardai said the woman's body was discovered at the Bective House complex, Beaufort Place, Navan at about 7pm.
She was also aged in her 30s.
Gardai said staff from the State pathologist's office have been called in to inspect the scene while the body remained there.
Forensic examinations are also taking place in the apartment.
Gardai said the arrested man was taken to hospital for treatment.
Officers appealed for anyone with information to contact them in Navan station.
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