Fujimori has been in Chile since 2005 and is under house arrest in the capital Santiago.
Peru accuses him of embezzling millions of dollars and of human rights abuses including involvement in two massacres during Peru's battle with the Shining Path Maoist rebel group.
He denies all the charges against him.
The 68-year-old fled to Japan - the country of his parents' birth - after his government collapsed in 2000 in the wake of a huge corruption scandal. He lived there for five years.
He recently announced he intended to run in this month's Japanese senate elections, a move dismissed by his critics as a ploy to avoid extradition from Chile.
Alvarez' verdict came as something of a surprise.
Two weeks ago, when Fujimori announced his plans to seek election in Japan, analysts said it would not necessarily save him from extradition, even if he were granted parliamentary immunity as a result.
The ruling is likely to anger Fujimori's critics.
The former president won praise for his tough stance on terrorism, particularly for the way he handled a four-month siege of the Japanese ambassador's residence in Lima in 1996-97, but he was also criticized as undemocratic after he shut down the Peruvian congress in 1992.
In Lima, a spokesman for Fujimori hailed "a good day for Fujimori-ism".
Speaking to local radio station RPP, Carlos Raffo, a Peruvian congressman, said: "This is the first verdict and it certainly suggests to us things are going in the right direction ... but we are going to remain prudent and cautious."