Probably, yes. Depends on how good the shielding is on your monitor.
If the shielding is not great, it will interfere with yoke (I think that
is what is happening. Someone else correct me.)
When that happens your monitor will show miscoloration or
misalignment. And I believe that you can magnetize some part
of the monitor, probably the grill. And once that is magnetized,
I have seen it be permanent.
So... best way to test is move the speaker *SLOWLY* close to the
monitor where you want it. Put a bright screen up for the background,
perhaps a white background. If you see any miscoloration, pull them
away fast.
Some speakers are so low in magentic field, or are good enough in
shielding that it won't hurt. But in many cases, you can permanently
damage your monitor.