June 9 (Reuters) - Shares of Australia's "Big Four" banks fell further on Thursday to hit multi-month lows, as the central bank's largest interest rate hike in 22 years earlier this week sparked fears of a sell-off in the housing market.

These concerns have begun to grow as home prices snapped a 20-month winning streak in May amid rising rates and a cost-of-living crunch.

"Locally, the banks are being pressured by the outsized rate hike from the RBA (Reserve Bank of Australia) and the prospects that this will weigh too heavily on the housing market and their profitability," said Kerry Craig, a global market strategist at JP Morgan.

"However, given elevated levels of household leverage in Australia, the market is taking a dim view of the ability of households to contend with higher servicing costs."

Commonwealth Bank of Australia (CBA.AX), National Australia Bank (NAB.AX), Westpac (WBC.AX) and Australia and New Zealand Banking Group (ANZ.AX) tumbled between 2.6% and 3.7%, dragging the benchmark index (.AXJO) to a three-week low.

The RBA on Tuesday lifted its cash rate by 50 basis points to battle soaring inflation, and investors are wagering that rates will rise to near 3% by the end of 2022, making it one of the most aggressive tightening campaigns on record.

The country's major lenders followed suit and raised home loan variable interest rates by 50 basis points per annum.

"Rising rates and fading growth outlook are dragging the property sector lower. We can already see lower prices and weaker demand for loans," said Mathan Somasundaram, chief executive officer at DeepData Analytics.

"Banks have benefited from cutting bad debt provisions to boost profits in recent years. We expect these to reverse."

Rising rates also appear to have made bonds attractive to investors, with the yield on Australia's 10-year note hitting its highest in nearly eight years.