Arsenal issued a statement saying Kroenke, who joined the club's board last year and became the largest shareholder in May, paid 1.5 million pounds for another 160 shares at 8,500 pounds each.
Kroenke has leapfrogged Russian billionaire Alisher Usmanov, who was the largest shareholder with about 25 percent.
The American businessman's shareholding is now close to the 30 percent threshold that would force him to make an automatic offer for the remaining shares, although he has previously said he is not interested in pursuing a full buyout.
Arsenal have been at the centre of takeover speculation after Kroenke and Usmanov started building stakes.
Earlier this week Usmanov offered to invest 60 million pounds for the club to spend in the transfer market, but his plan was rejected by the club's board.
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