The single-seat aircraft fell off the radar at 6:43pm (10:43 GMT) while it was conducting regular nighttime training, the ministry said in a statement.
It was flown by Ho Tzu-yu, an experienced captain who graduated from the Air Force Academy in 2013 and has accumulated more than 700 hours of flight time, it added.
Of his flight experience, 491 of those hours were flying the Mirage-2000.
The air force has dispatched a S-70C rescue helicopter and C-130 transport aircraft to the waters where the fighter jet had disappeared, the ministry said.
"We hope to find captain Ho Tzu-yu as soon as possible during this golden period tonight," said Chang Yan-ting, an air force spokesman.
A total of six vessels from the military and the Coast Guard Administration are also being sent to join the rescue operation, according to Chang.
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