Later this month K1, an additional exhibition space for the Finnish Museum of Photography, will open right downtown, in the Kamp Shopping Center at Pohjoisesplanadi 33. The hours will be longer than usual for Finnish museums--11 AM to 8 PM daily, and (unlike the main location) it apparently doesn't plan to close over the Midsummer weekend. The regular entry fee will be €12, but just €5 for students and seniors.
The inaugural exhibition will be "Marilyn [Monroe] and Coco [Chanel]": https://www.valokuvataiteenmuseo.fi/en/k1s-inaugural-exhibition-marilyn-coco
I don't know for sure that this new space will be covered by the Helskinki Card, but the FMP itself is covered.