Kravet måste vara skriftligt.

Because -et is the definite article suffix for many neuter nouns in Swedish.

• ett krav = a requirement
• kravet = the requirement

So Kravet måste vara skriftligt means you are talking about a specific requirement: the requirement.

Swedish usually puts the definite article at the end of the noun instead of using a separate word like the.

Swedish main clauses usually follow the V2 rule, which means the finite verb comes in second position.

In this sentence:

• Kravet = first element
• måste = finite verb, so it comes second

That is why the sentence is:

• Kravet måste vara skriftligt

and not something like:

• Kravet vara måste skriftligt

The normal basic pattern is:

• subject + finite verb + infinitive/adjective/etc.

Because måste is a modal verb, and modal verbs are followed by the infinitive form of another verb.

Here:

• måste = must
• vara = infinitive of to be

So the structure is:

• måste vara = must be

This is very similar to English:

• must be

Other examples:

• Du måste läsa. = You must read.
• Det måste fungera. = It must work.

Because skriftligt agrees with the noun kravet, and krav is a neuter noun.

The adjective skriftlig changes form depending on the noun:

• en skriftlig ansökan = common gender singular
• ett skriftligt krav = neuter singular
• skriftliga krav = plural

Since kravet comes from ett krav, the adjective must take the neuter singular form:

• skriftligt

So:

• Kravet måste vara skriftligt is correct.

Because Swedish usually expresses definiteness by adding an ending to the noun.

So instead of:

• the requirement

Swedish says:

• kravet

This is very common in Swedish:

• boken = the book
• huset = the house
• kravet = the requirement

Sometimes Swedish also uses a separate definite word, but that usually happens when there is an adjective before the noun:

• det skriftliga kravet = the written requirement

In your sentence, there is no adjective directly before the noun, so kravet by itself is enough.

It is best understood as an adjective, specifically a predicate adjective.

In the sentence:

• Kravet måste vara skriftligt

the adjective comes after vara and describes the subject kravet.

This works like English:

• The requirement must be written

Even though it comes after be/vara, it is still describing the noun, so it is not functioning like a normal adverb.

Yes, but it means something slightly different.

• Kravet måste vara skriftligt = The requirement must be in writing / must be written
• Det måste vara skriftligt = It must be in writing / It must be written

With det, the sentence is more general or depends more on context. You need to know what det refers to.

With kravet, the sentence clearly names the thing being discussed.

Yes, but the nuance changes.

• måste vara = must be
  This sounds stronger and more like a firm necessity or rule.

• ska vara = is to be / should be / must be depending on context
  This can also express a rule, but sometimes it sounds more like an instruction, expectation, or official requirement.

In many formal contexts, both are possible, but måste often feels more explicitly necessary.

Yes, it sounds fairly formal and would fit well in legal, administrative, or official contexts.

Words like:

• krav
• skriftlig

are common in formal Swedish.

In everyday speech, people might sometimes choose a less formal wording depending on the situation, but this sentence itself is completely natural and correct, especially in official language.

In this kind of sentence, skriftligt often means something like in writing or written down in written form.

So Kravet måste vara skriftligt usually means the requirement must exist as a written statement or document, not just be said orally.

In legal or administrative English, must be in writing is often the most natural translation.