The rights group said 9,000 people have already been forced from their homes during the first phase of the plans.
"The effects of February's forced eviction have been devastating," said Amnesty's Oluwatosin Popoola.
A local official told the BBC that displaced residents would get priority when new houses became available.
Slums have sprung up all over Lagos as a result of people pouring into the overcrowded city in search of work.
Amnesty has published satellite images showing what it said was "a densely populated area'' that was razed to the ground in February.
The group said it took the images to disprove claims by government officials that the affected area was a rubbish dump.
Amnesty said residents were now sleeping in the open, at risk of disease and bandits, and that thousands of people have lost their livelihoods along with their homes.
The report calls on Lagos authorities to halt the forced evictions.
The BBC's Will Ross, in Lagos, says the sight of bulldozers moving into slum areas at dawn and flattening people's homes is a familiar scene, happening more and more in cities across the continent.
Bringing some order to this chaotic city of more than 15 million people is a huge challenge for the state government, our correspondent says.
Critics say the wealth gap is widening as those forced from their homes can only dream of owning an apartment in the new developments that are replacing the city's slums.
"We want the state government to remember that we are not animals," Tunde Aworetam, a pastor in the affected community, is quoted as telling a press conference.
One woman who was evicted told the BBC's Focus on Africa programme that she had gone to the local government, but did not expect any support.