The verdict is scheduled for 18 July.
Mr Navalny, a 37-year-old anti-corruption campaigner, later denounced President Vladimir Putin's rule, saying his system was "sucking the blood out of Russia".
If convicted, he could be kept in prison until after the next presidential election in 2018.
The prosecutors stopped short of demanding the maximum term of 10 years at the trial in Kirov, a city 900km (560 miles) north-east of Moscow.
Mr Navalny denies defrauding a timber firm of 16m roubles (Â£300,000; $500,000).
In a live webcast from the courtroom, Mr Navalny said he and his colleagues "will do our best to destroy the feudal state that's being built in Russia, destroy the system of government where 83 per cent of national wealth is owned by half a per cent of the population''.
"If somebody thinks that upon hearing this threat of six years, I will run away abroad or go into hiding, they could not be more wrong,'' he said. "I don't have any other choice and I don't want to do anything else. I want to help the people of my country, work for my compatriots."
He inspired mass protests against the Kremlin in December 2011, and recently declared he would like to stand for president.
He is currently campaigning for election as mayor of Moscow in September.
He says the case has been fabricated to remove him from politics.
When the six-year demand was announced, Mr Navalny looked shocked and exchanged nervous smiles with his wife Yulia, who then embraced him when a short break in proceedings was declared, Reuters news agency reports from Kirov.
"I still hope everything will be fine," Mr Navalny told reporters.
The case against him is one of five opened by investigators in the year since Vladimir Putin was re-elected president.
He is accused of defrauding the Kirovles state timber company while working as an adviser to Kirov's governor, Nikita Belykh.
The judge in his trial has not acquitted anyone in more than 130 cases.
Russian prosecutors have called for a six-year prison sentence for opposition leader Alexei Navalny, on a controversial charge of embezzlement.