Use x(x < threshold) = 0, where x is your signal and threshold is your noise amplitude. Or x(abs(x) < threshold) = 0, if you meant the amplitude of the signal is below the noise amplitude.
Here's a concrete example:
% random signal
x = 0.25*rand(1,20);
plot(x,'-o');
hold on
% set values below 0.1 to 0:
x(x < 0.1) = 0;
plot(x,'.-');
legend({'original' 'new'})
