The party later said that IT officials had given them access to funds in the accounts pending a hearing in court.
Congress leader Mallikarjun Kharge called the freezing of funds as an "assault on democracy".
The government or the IT department have not responded to the allegations.
Congress leader Ajay Maken told reporters on Friday morning that the party had been informed two days ago that the cheques it was issuing were "not being honoured" by banks.
On investigating, the party was told that "all its accounts had been frozen".
Mr Maken said that the money in the party's accounts had come through online crowdfunding while that in it's youth wing's accounts had come from membership fees. He said that accounts of its youth wing - Indian Youth Congress - had also been frozen.
"We don't have any money to spend, to pay electricity bills, to pay salaries to our employees," Mr Maken said and added that all political activities of the party will be impacted.
He said that the action had been taken on account of a 45-day delay in filing income tax returns of the party for 2018-2019.
He added that the IT department has asked Congress to pay 2.1bn rupees ($25m; £20m) as a "recovery" amount.
Congress leader Vivek Tankha has said the court will hear the party's appeal for interim relief from the IT department's action on Wednesday.
Critics have accused Narendra Modi's Bharatiya Janata Party (BJP) of using state machinery to target opposition leaders in the run-up to the elections. Mr Modi and the BJP have denied the allegation.
BBC