Ministr pracuje na ministerstvu.

Because na here is followed by the locative case when it means in/at a place.

The basic dictionary form is ministerstvo.
After na for location, it becomes na ministerstvu.

• nominative: ministerstvo
• locative singular: (na) ministerstvu

So na ministerstvu means at the ministry / in the ministry.

It is the locative singular.

In this sentence:

• Ministr = subject, so it is in the nominative
• pracuje = verb
• na ministerstvu = location, so ministerstvu is in the locative after na

A useful pattern to remember is:

• na + locative = location: at/on/in
• na + accusative = motion toward something: onto/to

For example:

• Je na ministerstvu. = He is at the ministry.
• Jde na ministerstvo. = He is going to the ministry.

This is mainly a matter of Czech usage and collocation: certain places are idiomatically used with na, not v.

With institutions and workplaces, Czech often prefers na:

• na ministerstvu = at the ministry
• na univerzitě = at the university
• na poště = at the post office

English speakers often expect v because it can mean in, but Czech does not always match English preposition choices directly.

So the best approach is: learn the phrase as a unit, pracovat na ministerstvu.

Because the Czech word is ministr, not minister.

Although it looks similar to English, the Czech noun has its own form:

• ministr = minister
• ministerstvo = ministry

These two words are related, but they are not the same word in different cases.
They are two separate nouns.

Pracuje is the 3rd person singular present form of the verb pracovat = to work.

So pracuje can mean:

• he works
• she works
• it works

In this sentence, the subject is ministr, so it means the minister works.

A few present-tense forms of pracovat:

• pracuji / pracuju = I work
• pracuješ = you work
• pracuje = he/she works
• pracujeme = we work
• pracujete = you work
• pracují / pracujou = they work

Because Czech does not have articles like English a and the.

So ministr can mean:

• a minister
• the minister

And ministerstvu can mean:

• a ministry
• the ministry
• depending on context, often the ministry

Czech usually leaves definiteness to context rather than using a separate article.

Yes. Czech word order is more flexible than English because grammatical roles are often shown by endings, not only by position.

The neutral order here is:

• Ministr pracuje na ministerstvu.

But other orders are possible, for example:

• Na ministerstvu pracuje ministr.
• Pracuje na ministerstvu ministr.

These do not usually change the basic meaning, but they can change emphasis or what sounds new/important in the sentence.

The version you have is a very natural, straightforward word order.

No. Czech often omits subject pronouns when they are not needed.

Because the verb ending already shows the person and number, and because the noun ministr is present, there is no need to add on.

So:

• Ministr pracuje na ministerstvu. = natural
• On pracuje na ministerstvu. = possible, but now he is emphasized

Czech uses pronouns more sparingly than English.

A rough pronunciation guide is:

MIN-istr PRA-tsoo-ye na mi-nee-STER-stvoo

A few important points:

• Czech stress is usually on the first syllable of each word:
  • MInistr
  • PRAcuje
  • NA
  • MInisterstvu
• c is pronounced like ts
• j is pronounced like English y
• u is like oo in food

So pracuje sounds roughly like PRA-tsoo-ye.

Yes, ministr is a masculine animate noun.

That matters in Czech because gender affects:

• adjective endings
• pronouns
• some past-tense forms
• case endings in many situations

In this sentence, you do not see many obvious gender effects yet, but it is still important to know the noun’s gender.

For example:

• ten ministr = that minister
• nový ministr = a new minister

Because ministr is masculine animate, it behaves like other masculine animate nouns in Czech grammar.