Macs don't have mic-in (microphone input) jacks, they only have line-in jacks. Line-in jacks are "line level" audio input jacks, for receiving moderately amplified audio signals from another independently-powered piece of audio equipment like an audio CD player. Line-in ports expect power levels about an order of magnitude stronger than microphones usually provide.
Using the earpiece of a headphone as a makeshift microphone might kinda-sorta work, albeit at very low quality, on a mic-in jack, but it would never work on line-in. Even with very large over-the-ear headphones, the amount of power generated by your vocal sound waves vibrating the speaker cone to move the speaker coil through the magnets would be far too little to really register on a line-in jack.
Like jcomeau_ictx suggested, you can get a pre-amp for a microphone that amplifies the signal from mic-level to line-level. Or as NReilingh suggested, you can get a USB microphone that has it's own ADC (Analog to Digital Converter), so it basically acts as its own mic-in jack and sound input card.
If you have headphones that contain a built-in mic, you might be able to get that built-in mic to work on the headphone jack of your Mac mini, as long as the tip/ring/sleeve "pinout" of your headphones' 3.5mm phono plug matches the way Apple does the pinout for their iPhone headset with microphone.
(I feel like I've just consolidated and expounded upon what the other Answers have said, without adding much of my own, so feel free to vote them up instead of me.)