The open letter from Uzbek-born billionaire Usmanov, who has a stake of just under 30 percent, makes public his concerns over the running of the Premier League club, majority owned by American Stan Kroenke.
"It is down to our manager, and not the shareholders, to have to deal with the club's tight finances, carry the burden of repaying the stadium debt by selling his best players and having to continue to find cheaper replacements," he said.
Manager Arsene Wenger learned on Wednesday that striker Van Persie, who scored 37 goals last season, would not renew his contract when it expires next year.
"Yet again we are faced with losing our true marquee player at the club because we cannot assure him of the future direction and give confidence that we can win trophies," added Usmanov, who pointed out that his Red & White Securities group had invested around 200 million pounds in the club.
Arsenal have not won a trophy since 2005 but their third-place finish last season was enough to guarantee them a place in the lucrative European Champions League for the 15th successive season.
The club confirmed they had received the Usmanov letter and said they were considering its content.
Arsenal's policy is to be self-funding and the club believe they are well placed to benefit from new Financial Fair Play rules designed to ensure leading European clubs clean up their finances.
Arsenal had a pretax profit of 49.5 million pounds in the six months to November 2011, figures boosted by the sales of Cesc Fabregas to Barcelona and Samir Nasri to Manchester City.
The north London club pay annual interest of around 20 million pounds on debt linked to their move to the 60,000-seater Emirates Stadium in 2006.
Usmanov said Arsenal had to match clubs such as Chelsea, Manchester City, Real Madrid and Barcelona financially if they were to compete with them on the field.
Champions League winners Chelsea and Premier League winners Manchester City are bankrolled by wealthy owners, while the Spanish duo are helped by being able to sell their own broadcast rights.
Usmanov, who does not have a seat on the Arsenal board, said Red & White Securities had a vision of a debt-free club with enough money to buy top players.
He said the group would buy more shares from anyone who wanted to sell them and was committed to a long-term investment.
