You can do it this way:
%// Example plot
x = 1:10;
y = randn(1,10);
plot(x,y)
%// Marker at minimum
[ymin imin] = min(y);
xmin = x(imin);
hold on
style = 'ro'; %// red circle. Change as needed
markersize = 10; %// change as needed
plot(x(imin), ymin, style, 'markersize', markersize)
%// Text with coordinates of minimum
offset = -.05; %// vertical offset as a fraction of y-axis span. Change as needed.
text(x(imin),ymin+diff(ylim)*offset,['(' num2str(x(imin)) ',' num2str(ymin) ')'])
%// Enlarge y axis so that text is properly seen, if offset is negative
ylim(ylim+[diff(ylim)*offset*(offset<0) 0])
You might also want to enlarge the x axis if the text is close to the left or to the right. It could be done with xlim
in a similar way.