On Tuesday, he resurfaced at a secret air defence base on the remote Novaya Zemlya archipelago in the Arctic Ocean, Navalny said.
"He has been unlawfully deprived of freedom," President Vladimir Putin's top opponent said in a blog post, calling the 23-year-old a "political prisoner".
The Russian military insisted that Shaveddinov had been dodging the draft for a long time.
Russian men are eligible for conscription between the ages of 18 and 27 and serve one year's military service. However, many find ways to avoid this in a highly corrupt, flawed system.
Navalny said Shaveddinov has a medical condition that disqualifies him for military service but he was forcibly drafted and sent to the Arctic base without basic training.
Vyacheslav Gimadi, a lawyer for Navalny's foundation, said Defence Minister Sergei Shoigu and commander-in-chief Putin were directly responsible for what he claimed was an act of "kidnapping".
Navalny's spokeswoman Kira Yarmysh, who is Shaveddinov's partner, said the project manager had recently acted as a contact person for opposition lawmakers in Moscow city parliament.
"Perhaps this is the reason this has happened," Yarmysh told AFP.
She said Shaveddinov had managed to call her from Novaya Zemlya using other people's phones.
Navalny said Shaveddinov was not allowed to communicate with the outside world or use a phone, unlike other servicemen.
The military also assigned a man to follow Shaveddinov all the time, he added.
"The armed forces themselves don't know what the hell they should do with him," Navalny said.
Putin's spokesman Dmitry Peskov told reporters he did not know whether Shaveddinov had been dodging the draft, but said "If he had and was drafted in this manner then everything was done in strict accordance with the law."
Authorities have been steadily ramping up pressure on Navalny and his allies in recent years.
The 43-year-old helped organise major protests against the government this summer when tens of thousands took to the streets of Moscow to demand fair elections.