Osborne said he would not give the green light to the sale until turbulence in global markets had subsided.
In a tweet, Osborne said: "We'll build a share owning democracy. So British people can buy Lloyds shares but we'll only sell when turbulent markets have calmed down."
David Cameron pledged during the general election to sell the final part of the government's stake, which was expected to raise £2bn.
Details of the sale - set be one of the biggest privatisations since British Gas and BT in the 1980s - were announced last October.
It was hoped that the sale would happen in the spring, but banks have faced tougher trading in the wake of the market turmoil caused by a slowdown in the Chinese economy.
The government bought Lloyds shares for 74p when it used taxpayers' money to bail out the bank as it looked to bring stability to the industry at the height of the financial crisis.
However, the Lloyds share price has fallen from 78p to 64p since October, meaning shares would have been sold at a substantial loss.
The government owns just under 10% of Lloyds and 73% of the Royal Bank of Scotland.
The announcement poses questions as to whether the chancellor will now put on hold any plans to sell its remaining stake in RBS.