Provide security within the Ministry
After the fall of the Ministry of Magic, the Ministry Police issued the Undesirable No. 1 posters for information on the whereabouts of Harry Potter. During the Death Eater regime, members of the Ministry Police were stationed at the Atrium and arrested Muggle-borns who arrived at the Ministry. They were also in charge of transporting convicted Muggle-borns from the courtrooms. Each member wore a dark red strip of fabric around his or her left arm, signifying their position. These armbands were also worn by Snatchers, suggesting a possible connection between the two groups. 
Behind the scenes
- While it is likely that the Ministry of Magic indeed have some sort of unit of security wizards tasked with providing security services, the existence of a Ministry Police can not be considered canon, due to the fact that Amos Diggory was unfamiliar with the word "policemen", something that would not have been the case if the Ministry, where he worked, had their own inter-ministerial 'police' force.
- Harry Potter and the Deathly Hallows: Part 1 (First appearance)
- LEGO Harry Potter: Years 5-7 (As "Ministry Guard")