Voldemort filled Harry's mind with visions of Sirius dying in the Department of Mysteries, to lure Harry there.
This was because the prophecies were enchanted so that only the people referred to could lift them from the shelves. Albus Dumbledore:
‘Only the people to whom they refer can lift [prophecies] from the shelves without suffering madness ...’
But the prophecy also referred to Voldemort, at least as much as Harry! Why couldn't he just go and take the prophecy off the shelf?
An analysis of the prophecy
The one with the power to vanquish the Dark Lord approaches That's a reference to Voldemort
Born to those who have thrice defied him The 'him' is Voldemort
Born as the seventh month dies
And the Dark Lord will mark him as his equal, but he will have power the Dark Lord knows not Clearly referring to Voldemort
And either must die at the hand of the other for neither can live while the other survives and again. This line also means that the prophecy is also about Voldemort as well as Harry, rather than just referring to him.
The one with the power to vanquish the Dark Lord will be born as the seventh month dies and yet again.
Voldemort was referred to on almost every line of the prophecy.
Why did he need Harry to take the prophecy off the shelf?