Zofija Kaczan suffered multiple injuries in the attack on 28th May and died in the early hours of Wednesday morning.
Derbyshire Police said a 39-year-old man who had previously been arrested on suspicion of robbery has now been arrested on suspicion of murder.
He remains in custody and is being questioned.
Ms Kaczan was approached from behind, knocked over and had her handbag snatched at 8.45am, close to the junction of St Chads Road and Empress Road in Normanton, Derby.
The bag, made of green fake leather with gold clasps, was found at the junction of Moore Street and Normanton Road.
She was left with a fractured cheekbone but managed to stumble into St Maksymilian Kolbe Polish Church, still clutching one of the bag's straps.
Police are still keen to speak to anyone who saw a beige Seat Leon car seen close to the scene of the mugging and found abandoned two days later.
Officers are appealing for anyone with dashcam or CCTV footage that shows the vehicle with the registration plate SL02 KVZ to come forward.
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