Democracy does exactly that - it gives everyone the same vote, regardless what minority they come from. Therefore, it protects
any minority for maximum possible extent. You don't need any formal rules on top of that; in other words, the solution to "tyranny of the majority" should not be "tyranny of the minority". (I really hate the phrase "tyranny of the majority", by the way, because it simply isn't a good way to describe democratic voting, where the majority is emergent and not determined ex ante.)
But let's say, indeed, majority wants to violate the rights of minority. Stripping other people from voting rights isn't democratic (even if it's voted by everybody), because it violates the basic democratic rule, "every person should get the same power in politics". Democracy is defined by the end result (same access to power), not the procedure (voting). (In fact, democracy allows for tradeoffs where a person gets little more power in exchange for more accountability.)
It's true that even without stripping other voter's rights, minorities can still be persecuted. But it is a cultural issue, which won't be resolved by formal constitutional framework. In fact, historically, it very often were elites (that you may think are the solution) who participated or even organized these persecutions.
For example, in the U.S., there is a large minority of people in prison who are not protected by democracy, because they don't have voting rights. I would appreciate proof of any claim as to how any sort of republican institutions in the U.S. helps these people be protected. I don't see that.
Someone wrote below that the solution could be super-majority vote, like 80% of citizens to agree to change the constitution. I think that's a wrong idea, which doesn't give enough credit to people. This can possibly protect a minority, but it can also delay progress in helping minority. The minority that needs to be overruled in super-majority voting can keep the status quo longer than desired by most, and that's unfair too. We don't know what the future morality will be; it may be different in positive, not negative, fashion compared to today's morality. We could perhaps say, though, that the future society will be more happy with their own morality than ours (because they can compare the two, we cannot); therefore, it should be possible for them not be too conservative and implement it.
Anyway, this debate is always rather academic, because politicians only rarely vote with the majority. (And no, pre-war Germany is not a good example, as I already explained above.)