In Harry Potter and the Deathly Hallows, the ministry of magic was infiltrated by Voldemort and Death Eaters so that Voldemort and Death Eaters could take control of the ministry. However, Order of the Phoenix was also another resistance force against Voldemort and Death Eaters. Why didnt Voldemort and Death Eaters do anything to infiltrate the Order?
The Order was insignificant.
By the time Voldemort had taken control of the Ministry, the Order was basically a non-entity. Consider that of the 22 members of the original Order mentioned in this answer 16 were dead or otherwise out of commission by this point. Even with the handful of people who only joined the Order the second time around, there would have only been about 10 members left. They had lost their leader (Dumbledore), and the replacement leader (Moody), and many of their best members.
Even at the height of the second Order's power, it wasn't much of a threat to Voldemort. Throughout Order of the Phoenix and Half-Blood Prince all we really see the Order do is guard the prophecy and try to secretly convince people that Voldemort had returned. By the time Voldemort controlled the Ministry those were both moot.
We don't really find any examples in the books of the Order actively doing anything to weaken Voldemort's side, and by this point they couldn't really have done anything if they tried. The remaining members were being watched, and they had very limited resources. When Lupin visited Harry and friends at Grimmauld Place he explained to them how the Death Eaters with the full might of the Ministry easily broke through all the Order's protective enchantments, and raided all Order related houses. Simply put, the Order was essentially powerless at this point.
Members of the Order even admitted that the battle was over and the Order had essentially ceased to exist. To quote Aberforth from Chapter Twenty-Eight.
"The Order of the Phoenix is finished. You-Know-Who's won, it's over, and anyone who's pretending different's kidding themselves.
So, simply put, Voldemort had no need to infiltrate the Order because the Order posed no real threat to him. The Ministry, on the other hand, was a threat to him if not under his control, and he therefore took control of it.
The Death eaters were able to infiltrate the Ministry of Magic for multiple reasons which were not true of the Order of the Phoenix. The Ministry was a large organization with hundreds (possibly thousands) of employees, making it extremely difficult to screen everyone that worked there for divided loyalties. More importantly, Minister Cornelius Fudge had convinced himself that Voldemort's return was a ruse by Dumbledore to discredit or oust him as Minister rather than a serious threat. His actions delayed any countermeasures that might have been taken until it was far too late.
The Order, on the other hand, was a very small organization that was certain of Voldemort's return and dedicated entirely to opposing him. In addition, Snape was providing information on the Order to Voldemort in his role as a double agent, so further infiltration did not seem necessary to the Death Eaters.