Typically, they didn't even have prisons for men in medieval times.

If you were considered guilty of a crime you were usually punished immediately - holding you for years was thought to be pointless. You'd be exiled, fined, humiliated, beaten, branded, mutilated, forgiven, or executed, but you wouldn't be thrown in a jail for 20 years or anything like that. Punishment was done in public and served as a warning against transgression and as a demonstration of power by whoever was meting it out.

The only people that would be held for a long time would be nobility, because generally they had some rich relatives who would be willing to pay for their release, and it was often considered taboo to execute royalty. In this instance, women would be held in similar facilities to men. This would usually be something decent - a tower in a castle, for instance, and they'd often be allowed full freedom of movement in the castle if they weren't considered particularly violent or dangerous.

A famous example is King Jean of France, captured by the English during the Battle of Poitiers. During his captivity he was allowed many freedoms, and was seen in public cavorting with his entourage, going on hunts, trading horses, etc. He was obviously a prisoner captured in war and not for any criminal activity, but his treatment gives a window into the medieval mindset of captivity. It was often on the captive noble's honor to not escape, and attempting to do so could ruin his reputation.

To arrest a noble for doing something criminal you'd need someone willing and able to arrest them, as there was nothing like a standardized police force at the time. This obviously differs across time and geography, but if a noble was to be punished it would usually involve loss of land/titles/money/goods/privileges which would then go to someone else - the noble wouldn't be given a sentence of ten years to serve their debt to society or anything. Their debt, if any, was tangible, and was paid in kind, rather than through sitting in a room alone until they became redeemed.

Women could of course be sent to convents by their families if they were considered troublesome, and this was a place to effectively imprison them, though you shouldn't consider it to be prison. Convents would vary in amenities and discipline as there wasn't any one way they were set up. One convent could be in a pastoral and safe environment with abundant food and comfortable domiciles, while another could be a leaky dump run by an abusive disciplinarian.