There seem to be, for the majority of countries at least, if not all.
It seems like there’s a Ministry of Magic in almost every country, though this is certainly not confirmed for sure. There may be some countries without many wizards that don’t have one, and there also may be some countries where the governing body of wizards isn’t called a Ministry of Magic but instead has a different name. However, at least from what we see, it seems like the majority of countries do have a Ministry of Magic.
The size of the country may have an effect on whether it has a Ministry of Magic, though it’s not really clear. There’s only one very small country that is said to possibly have one. Andorra, a very small country, likely has its own Ministry of Magic. (“Likely”, not “certainly”, because Barty Crouch Sr. was losing his mind when he happened to refer to their Ministry, so his words shouldn’t necessarily be considered true, though they still might be.)
“Yes, my son has recently gained twelve O.W.Ls, most satisfactory, yes, thank you, yes, very proud indeed. Now, if you could bring me that memo from the Andorran Minister for Magic, I think I will have time to draft a response …”
- Harry Potter and the Goblet of Fire, Chapter 28 (The Madness of Mr Crouch)
There are Ministries of Magic in several countries in Asia; India, Pakistan, Bangladesh, Iran, and Mongolia - all fairly large countries, so doesn’t prove that all countries have one.
“Quidditch has never achieved great popularity in the East, as the flying broomstick is a rarity in countries where the carpet is still the preferred mode of travel. The Ministries of Magic in countries such as India, Pakistan, Bangladesh, Iran and Mongolia, all of whom maintain a flourishing trade in flying carpets, regard Quidditch with some suspicion, though the sport does have some fans among witches and wizards on the street.”
Quidditch Through the Ages
There’s one in New Zealand. It’s (never mentioned whether Australia has one, though they do have Quidditch teams, so there’s likely some form of wizarding government, even if it’s not called a Ministry of Magic.
“The New Zealand Ministry of Magic has certainly spent much time and money preventing Muggles getting hold of Maori art of that period which clearly depicts white wizards playing Quidditch (these carvings and paintings arc now on display at the Ministry of Magic in Wellington).”
Quidditch Through the Ages
There’s one in Germany as well. (In articles on Pottermore written by JKR, there are said to be Ministries of Magic in France, Liechtenstein, and the question already refers to the one in Bulgaria.)
“Strict controls by the German Ministry of Magic, however, have reduced Erkling killings dramatically over the last few centuries and the last known Erkling attack, upon the six-year-old wizard Bruno Schmidt, resulted in the death of the Erkling when Master Schmidt hit it very hard over the head with his father’s collapsible cauldron.”
- Fantastic Beasts and Where to Find Them (textbook)
There’s also one in Norway.
“Kneen’s letter is deposited in the archives of the Norwegian Ministry of Magic.”
The countries we know for certain to have Ministries of Magic are all fairly populous. It’s unclear whether the much smaller and less populated countries, like Tuvalu, with a population of less than 10,000, would also have a Ministry of Magic or if there needs to be above a certain number of wizards before a country gets its own Ministry of Magic.
The Fantastic Beasts movie shows the USA has MACUSA instead.
In the Fantastic Beasts and Where to Find Them movie, we see the American wizard government, which is called the Magical Congress of the United States of America, usually abbreviated to MACUSA. While the organization itself was featured in the movie, its background was published on Pottermore.
MACUSA was modeled on the Wizards’ Council of Great Britain, which predated the Ministry of Magic. Representatives from magical communities all over North America were elected to MACUSA to create laws that both policed and protected American wizardkind.
The Magical Congress of the United States of America (MACUSA) (Pottermore)
Instead of a Minister of Magic, MACUSA is led by a president.
“High up, a gigantic dial with many cogs and faces emblazoned with the legend: MAGICAL EXPOSURE THREAT LEVEL. The hand on the dial points to SEVERE: UNEXPLAINED ACTIVITY. Behind hangs an imposing portrait of a majestic-looking witch: SERAPHINA PICQUERY, MACUSA’s President.”
Fantastic Beasts and Where to Find Them: The Original Screenplay
However, it has the same purpose as a Ministry of Magic would: enforce the laws of the wizarding world and ensure that wizards are not discovered by the Muggles.