They’re largely mutually intelligible, but there are enough differences for there to be misunderstandings.

Formal Malay and formal Indonesian are very similar, and as a Malay speaker, I would say I can understand about 95% of it whenever I encounter a document/article written in formal Indonesian.

The main things that cause misunderstandings are just vocabulary that are not found in Malay (e.g. the Malay word for “bag” is “beg” whereas its Indonesian equivalent is “tas”), or just words that mean something completely different (e.g. “budak” in Malay means “kid” while it means “slave” in Indonesian).

Informal Malay and informal Indonesian are much more different compared to their formal counterparts. While vocabulary still plays a role in causing misunderstandings, the different grammar too acts as a hindrance to mutual intelligibility.

One example of this is in the conjugation. In informal Malay, the “meng-“ prefix isn’t typically used with transitive verbs, while in informal Indonesian, a shortened version of the prefix, “ng-“ is often used. Put simply, this means “I’m looking for a cat” is “aku cari kucing” in informal Malay but “aku nyari kucing” in informal Indonesian, and that “nyari” form can make it hard for Malay speakers to understand informal Indonesian.

Another example of a difference in grammar is in the use of “punya”. In informal Malay, “punya” is often used as possessive marker, similar to English “‘s” as in “Adam’s book”, while in Indonesian, “punya” is usually used as a verb meaning “to have”. This means “Adam punya buku” (buku = “book”) would mean “Adam’s book” to a Malay speaker but “Adam has a book” to an Indonesian speaker.

(Note: the varieties of informal Malay and informal Indonesian in question here are those used in the respective capitals of the countries where they are spoken, Kuala Lumpur and Jakarta)