The Bank of Canada raised its overnight rate by a quarter-point Tuesday to 0.5%. It has become the first central bank in the Group of Seven rich industrial countries to tighten policy since the financial meltdown of 2008-2009.

While Canada’s economy expanded at a 6.1% clip in the first quarter, paced by rising consumer spending and house prices, conditions remain decidedly mixed elsewhere.

“The required rebalancing of global growth has not yet materialized,” the Bank of Canada said. “In most advanced economies, the recovery remains heavily dependent on monetary and fiscal stimulus.”

A weak and uneven global recovery will mean extra care in removing government support, the bank said. So don’t expect the Federal Reserve, Bank of Japan, or European Central Bank to rush to follow suit.

Indeed, economists at Bank of America Merrill Lynch are now forecasting the Fed won’t raise its fed funds rate from the current range of 0% to 0.25% till August 2011, thanks to debt worries in Europe and tightness in financial markets after stocks had their worst May in 70 years.

When euro worries ignited last month’s latest flight to Treasurys, the Canadian dollar sank against its U.S. counterpart after briefly trading at parity. A rise in Canadian rates could alter that equation, though the U.S. dollar may continue to strengthen on the assumption that Canada will move cautiously.

“The tone of the accompanying statement suggests that this is not necessarily the first step on a long march towards a normalization of interest rates,” said Paul Ashworth of Capital Economics in Toronto. “Nor are other G7 central banks likely to follow any time soon — the fundamentals in Canada are very different from those elsewhere.”