The grants will be delivered by Arts Council England on behalf of the Department for Culture, Media and Sport.
The Stephen Joseph Theatre in Scarborough was awarded the highest grant in the region, with £2.7m to be spent on essential repairs and upgrades to The McCarthy studio theatre and cinema.
The government said it would ensure the theatre could “continue to produce nationally significant productions and to provide local communities with access to live theatre”.
York Museums Trust will receive £2m to enable it to carry out repairs and prevent further water damage to the Grade I listed Yorkshire Museum.
Oakwell Hall in Kirklees will receive £1.6m of funding for work including stabilising the building, repairing the roof, replacing ceilings and gutters and relocating accessible toilets.
The full list of venues and services receiving funding are:
