A risk assessment by Transport for London identified sections of track where the noise from Tube trains affects nearby residents.
Ms Shawcross has urged TfL to use the delay to the Night Tube to carry out repairs.
TfL said it was "confident" local residents will not be disturbed.
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TfL's internal risk assessment was made public last month following a Freedom of Information request by The Times.
It found a four out of five chance that people living near to lines running at night would be "disturbed by noise, vibration and ground-borne noise".
The document also found that running trains at night could result in insufficient time to carry out maintenance, including rail-grinding, which helps keep tracks in good condition and reduces noise.
Ms Shawcross, Labour's transport spokeswoman on the Assembly, said: "When the Night Tube starts it will mean even more misery for those people living close to these sections of track who are already suffering from excess noise."
She recommended setting up a "noise-busters" team to respond to complaints and repair problematic sections of track.
Kevin Dunning, London Underground's network services director, said LU was carrying out hundreds of kilometres of rail-grinding in order to prepare for the launch of the Night Tube.
He said: "We're confident residents won't be disturbed and we'll of course continue to talk to anyone who has concerns once the service launches.
"The risk document was created to help us plan ahead and it's disappointing that Assembly members want to put a negative twist on this careful planning."
The Night Tube was originally due to begin operating in September last year but has been delayed due to ongoing disagreements between London Underground and unions representing drivers.
Labour London Assembly Member Val Shawcross has called for noisy parts of the Underground network to be fixed before the Night Tube service starts.