You can, but if you've customized the labels it's a bit trickier. Ideally you want to change the XTick and XTickLabel properties simultaneously, to keep them synchronized.
v = 1:10;
C = num2cell('A':'J');
h = plot(v, v.^2);
ax = ancestor(h, 'axes');
xt = ax.XTick;
labelsToKeep = [1:6 9:10];
ax.XTick = xt(labelsToKeep);
Because the tick labels were automatically generated, the tick labels remain unchanged as we jump from x = 6 to x = 9.
figure
h = plot(v, v.^2);
ax = ancestor(h, 'axes');
ax.XTickLabel = C;
xt = ax.XTick;
xtl = ax.XTickLabel;
labelsToKeep = [1:6 9:10];
ax.XTick = xt(labelsToKeep);
In this case, we don't jump directly from F to I. We "jump" from F to G. If your next line set XTickLabel appropriately, you may see a flicker if the display updates between those two lines.
ax.XTickLabel = xtL(labelsToKeep);
If you want to update them both at once, you can use set.
figure
h = plot(v, v.^2);
ax = ancestor(h, 'axes');
ax.XTickLabel = C;
xt = ax.XTick;
xtL = ax.XTickLabel;
labelsToKeep = [1:6 9:10];
set(ax, 'XTick', xt(labelsToKeep), 'XTickLabel', xtL(labelsToKeep));
In the case of the tick and tick label properties, changing the properties simultaneously isn't quite as important as if you were adding or deleting points by directly modifying the XData and YData properties. If the *Tick and *TickLabel properties are different lengths, MATLAB will compensate (only using the first part of the *TickLabel property or repeating the *TickLabel labels.) It's much more important to change the *Data properties together to avoid a warning.
figure
h = plot(v, v.^2);
x = h.XData;
y = h.YData;
labelsToKeep = [1:6 9:10];
h.XData = x(labelsToKeep);
drawnow
h.YData = y(labelsToKeep);
figure
h = plot(v, v.^2);
x = h.XData;
y = h.YData;
labelsToKeep = [1:6 9:10];
set(h, 'XData', x(labelsToKeep), 'YData', y(labelsToKeep));