It is possible but investigation will be strict than for Japanese.
If you don’t have a job (no stable income), it is almost impossible.
These days, the number of foreigners are increasing in Tokyo so there are a few companies who takes care of the the foreigner’s rental. But, it is still rare.
When you rent a house or a room in Japan, you usually need to pay 1 month deposit, brokerage fee (1 month rental fee), and Shiki kin/ Rei kin. Shiki kin/ Rei kin is Japanese traditional habit.
Shiki kin is a kind of security deposit (Max 2 months). Rei kin is gratuity fee (Max 2 months).
But, it will be paid back if you leave the house neatly and without damage.
Only one company, “Delta”, provides share houses for Filipinos in Tokyo and Kanagawa.
Delta is related to our organization. If you are interested, check the page of RENTAL PROPERTY page of Filipino Tokyo.