Norma Bell died overnight between 2 and 3 April prior to the blaze at her home on Westbourne Road, Hartlepool, Cleveland Police believe.
Detectives said a 32-year-old man was in police custody.
Officers believe a "substantial" amount of money is missing from her home. Mrs Bell had been due to celebrate her 80th birthday next month.
A man has been arrested on suspicion of murdering a 79-year-old woman found dead in her house after a fire.