The offer was a premium of 24% on the closing price of $2.98 on Friday, MYOB said in the statement. This would mean that KKR would pay about $1.75 billion for the company if its proposal was accepted.
MYOB said its board was examining the offer made by KKR.
It said an affiliate of KKR had bought 17.6% of its shares which had been held by Bain Capital Abacus Holdings, raising to 19.9% the interest held by KKR in MYOB.
MYOB chief executive Tim Reed said: "The board received this proposal over the weekend and we wanted to provide an update to the market immediately.
"We're working with our advisers to consider the terms of the non-binding offer and will keep the market informed as and when decisions are made.
"Our first commitment is, as always, to deliver exceptional shareholder value and therefore to consider any reasonable proposal.
"There is a lot of water to go under the bridge between this proposal and any potential resulting transaction.
"Early indications are that in KKR we have gained a supportive and interested shareholder who is confident in the company's strategy and people, as Bain were and we expect will continue to be with their remaining shareholding.
"While our board and advisers work through the next steps it is business as usual. We will continue to deliver on our strategy and to provide exceptional products and support for our clients and partners."