The party, however, did not say exactly when the Congress general secretary received the message.
This comes after WhatsApp revealed last week that Indian journalists and human rights activists were among roughly 1,400 users globally spied upon by unnamed entities using an Israeli spyware, Pegasus.
The messaging platform had said it sent special messages to all the affected users stating that it had "reason to believe they were impacted by this attack to directly inform them about what happened".
Over the past few days, several social activists in India have come forward and said they had received communication from WhatsApp in this regard.
"I want to tell that Priyanka Gandhi also received a similar message from WhatsApp around the same time," Congress chief spokesperson Randeep Surjewala said, responding to a question about NCP leader Praful Patel and West Bengal Chief Minister Mamata Banerjee receiving messages from the Facebook-owned messaging platform about the security breach.
Priyanka Gandhi received the message around the same time when WhatsApp was sending similar messages to those whose phones were allegedly hacked, Surjewala said.
"WhatsApp sent messages to different people whose phones were hacked. One such message was also received from WhatsApp on the telephone (mobile phone) of Priyanka Gandhi," he said.
"WhatsApp did not say that the phone was hacked in this fashion by an illegal Pegasus software," he said, adding that the nature of the message is already in the public domain.
The Congress spokesperson alleged that the government has adopted a "conspiratorial silence" on the matter and is hiding behind sources to plant stories in the media.
"A sinister role is being adopted by the government. The question is do people in India have a right to privacy and the rule of law or is right to privacy a joke to be trashed by Modi government as per its whims and fancies. This is a subject of far-reaching consequences," Surjewala said.
WhatsApp had said on Thursday that it was suing NSO Group, an Israeli surveillance firm, which is reportedly behind the technology that helped unnamed entities' spies hack into phones of the messaging platform's users.
These users span across four continents and include diplomats, political dissidents, journalists and senior government officials.
WhatsApp has over 1.5 billion users globally, of which India accounts for about 400 million.