He underwent further medical tests on Tuesday and skipped an appearance in parliament.
His spokesman said he was also suffering from tinnitus, sometimes described as ringing in the ears.
But Frederic Cauderlier told AFP news agency he would not give further details, in order to protect the prime minister's privacy.
The French-speaking Mr Michel hosted US President Donald Trump last week as he visited Brussels.
Princess Astrid, 54, is the younger sister of Belgium's King Philippe. The 20km (12.4 mile) road race on Sunday is an annual event and the princess took part alongside 40,000 other runners after pulling the trigger.
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