On Monday Jerusalem City Council approved the plan to demolish 22 Palestinian homes in Silwan - part of a major redevelopment of the area.
The move has drawn criticism both at home and from the Obama administration.
Mr Ban said the plan was "contrary to international law" and "unhelpful" to efforts to restart peace negotiations.
The scheme is still in an initial stage.
"The Secretary-General is deeply concerned about the decision by the Jerusalem municipality to advance planning for house demolitions and further settlement activity in the area of Silwan," Mr Ban's office said in a statement.
Israel's government had a "responsibility to ensure provocative steps [were] not taken" that would heighten tensions in the city, he said.
On Tuesday, the US State Department criticised the move, saying it undermined trust and increased the risk of violence.
Israeli Defence Minister Ehud Barak also criticised Jerusalem's municipality for "bad timing" and poor "common sense".
Under the plan, 22 Palestinian homes would be demolished to make room for an Israeli archaeological park. Another 66 buildings constructed without Israeli permission would be legalised.
Israel has come under international pressure over its settlement plans in East Jerusalem, including the construction of 1,600 housing units in a Jewish neighbourhood there.
Under international law the area is occupied territory. Palestinians want East Jerusalem as the capital of a future state.
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