Justice Tariq ul Hakim and Justice Md Faruque passed the order on Thursday after hearing a writ petition by a voter from Demra.
The Election Commission announced the polls schedule on Jan 9 after the death of former Dhaka North City mayor Annisul Huq.
The court has also issued a rule asking why it should not declare the schedule beyond the legal purview, said Deputy Attorney General Amatul Karim.
The EC was scheduled to hold the polls simultaneously to elect 18 councillors for the new wards in Dhaka North, as many in the south, and six others from the seats reserved for each of the two city corporations.
The High Court stayed the bypolls in Dhaka North and elections in new wards on Wednesday for three months on a writ petition filed by two UP chairmen.