You can set the corresponding values to NaN and change the color of the NaN values to white (or rather transparent) -
x=linspace(-2,2,300);
y=linspace(-2,2,300);
x2=x.^2;
y2=x.^2;
xy=x.*y';
U=1;
a=1;
vx=U*a^2*(x2./(x2+y2').^2-y2'./(x2+y2'));
vy=U*a^2*(xy./(x2+y2').^2+xy./(x2+y2'));
r=sqrt(x2+y2');
vx(abs(r)<1)=NaN;
vy(abs(r)<1)=NaN;
h = imagesc(x,y,vx);
set(h, 'AlphaData', ~isnan(vx))
colorbar
hold on
quiver(x(10:10:end),y(10:10:end),vx(10:10:end,10:10:end),vy(10:10:end,10:10:end),1.5,'k')
axis equal
xlim([-2 2])
ylim([-2 2])
