According to The Jakarta Post, the non-stop heavy rains started on New Year's Eve and continued into Wednesday.
State-owned electricity company PLN has temporarily cut power in 724 flood-hit areas in the capital to prevent incidents.
The media outlet added, citing Jakarta Governor Anies Baswedan, that over 19,000 people had fled their homes.
"The worst is in East Jakarta with 9,248 people [displaced], South Jakarta with 5,080", Baswedan was quoted as saying by the newspaper.
The floods have disrupted public transport with some railway lines temporarily closed. At least 10 flights were delayed at Halim Perdanakusuma Airport, which accommodates commercial and military aircraft. Many of them were redirected to Soekarno-Hatta Airport in Banten.