Checkup is a noun. It’s what you get when you visit your doctor for a routine examination. The word doesn’t work as a verb. When you need a verb, use the two-word check up. It’s one of many phrasal verbs with corresponding one-word nouns. For example, see also burn out and work out.
In British publications, checkup is often hyphenated—check-up—but the unhyphenated version appears as well.
Checkup is a noun—for example:
Alice just got back from a checkup with the doctor. [Forbes]
He was booked into the vets anyway for a checkup and vaccinations. [Stuff.co.nz]
Many feel overwhelmed and avoid checkups that could keep them healthy. [Dallas Morning News]
And check up is a verb—for example:
Luckily, there’s another way we can check up on how borrowers are doing — by considering delinquencies. [Atlantic]
If the blood test works, it will be an easier, faster way to check up on the disease in patients who’ve been diagnosed with MS. [Winnipeg Free Press]
The district gets monthly reports from providers and also checks up on them with unannounced visits. [Cleveland Plain Dealer]