It warns about what it calls "medium-term" dangers in both emerging and developed economies, in its twice-yearly report.
It expresses particular concerns about Europe, Japan and China.
On a more positive note, the fund does say that short-term risks have abated since its previous assessment of global financial stability in April.
Pressures on emerging markets have eased, the report says. Rising commodity prices (though they are still relatively low) have helped and so has the reduced uncertainty about China's prospects in the near term.
The report says investors were taken by surprise by the result of the British referendum on the European Union, but the political shock was absorbed by markets. They passed what it calls "this severe stress test".
But looking further ahead, the IMF sees growing risks.  A key factor is bank profits.
The good news is that banks are in some respects stronger than they were before the financial crisis. They have more capital, a kind of financial buffer that enables them to survive losses. Their liquidity has improved, which means they have more chance of coping if they suddenly have to find funds quickly.
But they are struggling to make money.
Weak profitability makes it harder for them to build up their capital (which they can do by holding on to some profit rather than giving it all to shareholders as dividends). It also makes it harder for them to expand lending to business and consumers, as is needed to support economic recovery.
The problems partly reflect the very low interest rate environment that developed-country banks have to operate in. The struggle to make profits also reflects the persistent economic weakness in the developed world, which means weaker demand for credit.
Some banks in the eurozone have a burden of problem loans, which are not being repaid and that they have still not dealt with.
The report identifies Italian and Portuguese banks as facing serious challenges of profitability and capital levels.
There is also a warning about Japanese banks and their expansion overseas, which the report says is the result of economic weakness and very low interest rates in their home market. That leaves them exposed to some risk in terms of access to the foreign currency funds they need to maintain that business.
The report warns about pension funds and insurance companies, whose position is also undermined by persistent low interest rates.
Outside the rich countries, China is seen as a potential trouble spot. The report says that rapid credit growth and the expansion of "shadow banking" (lending done by firms that are not banks) "pose mounting risks to stability".
The rapidly growing financial system in China is becoming increasingly "interconnected", the report says. The extent to which firms in the sector are interconnected - that is, have transactions with one another - was identified as a key factor in the financial contagion that was a feature of the international financial crisis.
The IMF's recommended medicine for these mounting risks is partly about generating a stronger economic recovery, including reforms to underpin growth. There are also calls for more specific financial steps, such as making it easier for banks to tackle problem loans and the banks themselves tackling high costs.
There's no sense in this report that another financial crisis is discernible on the horizon. But there certainly is a concern that the damage done by the last one is far from fully repaired.
The International Monetary Fund (IMF) has warned that risks to financial stability are growing.