Alexander, 51 and Britain's first black manager, suffered a brain aneurysm in November 2003 that kept him out of the game for six months.
Macclesfield's chairman Mike Rance said: "Keith had been feeling unwell in mid-week and though he came to the game, when he felt poorly again, on the advice of the club doctor he went for a brain scan. It's purely precautionary, just the safest possible option."
On the pitch veteran Lee Bradbury pulled Bournemouth further clear of the relegation zone with two clinical strikes.
After 56 minutes, he ghosted in from right-back to meet a long ball to the far post from Brett Pitman with a stunning volley from a narrow angle that crashed in off the far post.
And then after 70 minutes, Jeff Goulding again picked him out at the far post and though Macc keeper Jon Brain half-saved his shot it crept over the line.