This question Why didn't Voldemort curse the headmaster's position (if he was able to curse the DADA teacher position)? discusses the reason why Voldemort may or may not have wanted Dumbledore to lose the Headmaster job.
However, for functioning of any organization a leader is required. Their are several important posts in the ministry such as Heads of Magical Law Enforcement, Auror Office, International Magical Co-operation and ofcourse the Minister of Magic.
Constant change at the top is not helpful for the Magical Community and it has been repeatedly shown that Voldemort couldn't care less for the Statute for Secrecy if it helped him.
So why didn't Voldemort use this curse to cripple the working of Ministry?
Additionally, Could this have also worked for secret organizations? Such as the Head of Order of the Phoenix?