The speed limit on local roads at Green Square in Sydney's inner south will be cut to 40 kilometres an hour in the wake of a truck crash which killed one pedestrian and injured four others.

But the state's roads agency has resisted a push from the City of Sydney Council to extend the lower limit to busier routes in a precinct set to become Australia's most densely populated within a decade.

A 44-year-old woman was killed, and four other pedestrians injured, when a B-double truck veered off Botany Road at Green Square on Wednesday morning.

The City of Sydney said Roads and Maritime Services had granted conditional approval to reduce the speed limit to 40km/h on all local roads in the Green Square precinct, which encompasses Waterloo, Zetland and parts of Alexandria and Rosebery.