Fujimori said in a letter he intended to share thoughts and memories, happy and sad, while serving a 25-year prison sentence for human rights violations.
The social media accounts would be managed by a group of supporters.
The 75-year-old governed Peru for a decade before being impeached and fleeing the country in 2000.
Peru's Justice minister, Daniel Figallo, reacted angrily to Fujimori's announcement.
"People who commit violations and have their liberty taken from them have their rights limited. Otherwise, we turn prisons into hotels," he told reporters.
Mr Figallo reportedly asked the prison director to limit Fujimori's access to social media.
The former leader still has supporters in Peru and vowed to reveal his thoughts online.
"In this way, I'll be able to share my thoughts, memories and illusions,  sorrows and joys," his letter read.
Peru's President Ollanta Humala recently rejected Fujimori's request for a pardon on humanitarian grounds.
Earlier this week, the authorities rejected a bid by Fujimori's lawyer to have him  transferred to house arrest.
After being stripped of his powers by the country's Congress in 2000, the leader sought exile in Japan.
He eventually returned to Chile, where he was arrested in 2005.
After losing a lengthy legal battle, he was extradited to Peru in 2007 and convicted of human rights violations after a 15-month trial.
He was accused of authorising death-squad killings in two incidents known as La Cantuta and Barrios Altos, and the kidnapping of a journalist and a businessman.
Mr Fujimori repeatedly denied the charges, saying they were politically motivated.

Neville is still waiting for a first league win since taking charge of Valencia in December.
Former Barcelona B striker Sanabria, on loan from Roma, scored his fourth goal in two games after Danilo tripped Jony.
Alvaro Negredo missed three chances to equalise, heading one against the post, then chipping wide and blazing over.
Valencia, previously unbeaten at home in the league, then missed another great chance as Rodrigo Moreno and Sofiane Feghouli narrowly failed to connect with Zakaria Bakkali's left-wing cross.
At the other end, Australian goalkeeper Matty Ryan was fortunate not to concede a second penalty after barging into Carlos Carmona.
Valencia have not won any of the eight La Liga matches since former Manchester United and England defender Neville took charge and have gone a total of 11 league matches without a win, two short of equalling a club record.
Neville must attempt to lift his side in time for Wednesday's Copa del Rey semi-final first leg against Barcelona at the Nou Camp.
The former president of Peru, Alberto Fujimori, has said he will publish excerpts from his memoirs on the social media websites Twitter and Facebook.
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Gary Neville's Valencia were booed by their own supporters after Antonio Sanabria's penalty eased Sporting Gijon's relegation worries.