Party spokesperson Randeep Singh Surjewala said that Vadra’s phone was hacked with two other opposition leaders.
The other leader he said was Praful Patel, a former Union minister from the NCP.
Bengal CM Mamata Banerjee had on Saturday made a similar claim.
The party, however, did not say exactly when Gandhi received the message.
"I want to tell that Priyanka Gandhi also received a similar message from WhatsApp around the same time," Congress spokesperson Randeep Surjewala said, responding to a question about Praful Patel and Mamata Banerjee receiving messages from the Facebook-owned messaging platform.
Gandhi received the message around the same time when WhatsApp was sending similar messages to those whose phones were allegedly hacked, Surjewala said.
Stepping up the attack on the government, the Congress asked if the Narendra Modi dispensation spied on citizens and political leaders ahead of the 2019 parliamentary election.
Surjewala asked whether those sitting in the echelons of power are guilty of criminal offences and whether the government knew of the illegal spyware being deployed to spy on key persons.
"Shocking facts in #WhatsAppSpygate - Was BJP Government spying on citizens and political leaders in the run up to 2019 elections," he asked.
"Did Government know of the illegal spyware since May 2019? Are those sitting in echelons of power gulity of criminal offences," Surjewala asked.
WhatsApp had informed the Indian government in September that 121 Indian users were targeted by the Israeli spyware Pegasus, but IT ministry has contended that the information received from the messaging app earlier was inadequate and incomplete, according to sources.
Sources at WhatsApp said the messaging platform has now responded to the government's last week's query seeking an explanation on the Pegasus spyware incident that allegedly snooped on journalists and human rights activists across the world, including India.
(with inputs from PTI)