They were Reba's men.
Spoilers will follow.
This is the authorial intent, and this is what is implied in the novel. Boris Strugatsky acknowledged this explanation in an off-line interview:
Насколько я помню, дон Рэба имел целью захватить в плен Киру, дабы потом использовать ее как орудие шантажа. Замысел не удался, главным образом, из-за отвратительно низкой дисциплины его монахов (характерной, впрочем, для феодальных дружин всех времен и народов). Кроме того, дон Рэба никак не ожидал, что Румата, отъехавший давеча аж в пределы Пьяного леса, ухитрится каким-то загадочным образом оказаться дома.
Off-line interview with Boris Strugatsky about Hard to Be a God, question #5
If I remember correctly, don Reba's plan was to capture Kira and use her to blackmail [Rumata]. The plan failed, mostly because of the very weak discipline amongst monks' ranks (which was, by the way, present in most medieval brotherhoods). Moreover, don Reba did not expect at all for Rumata, having gone to the heart of the forest on the previous day, to be back home at this moment.
One could see that the men who stormed the house were monks:
“In the name of the Lord!” roared below. [...] There were numerous riders outside - sullen men in black with pointed hoods.
Hard to be a God, chapter 9. Translation by Olena Bormashenko, emphasis mine.
And that they did not anticipate for the owner of the house to be at home, but at the same time they knew very well it was Rumata:
“They always mess things up,” someone said softly downstairs. “The master’s at home.”
“What’s that matter to us?”
“It matters because he’s the best swordsman in the world.”
“And they also said that he left and won’t come back till morning.”
How can I tell? Because Rumata has been called the best swordsman in the world by our eagle don Reba, of all people. All this leads me to believe that it was don Reba who ordered Kira's abduction, but his monks messed it up.
Kira also says "they've come for me", in which she implies she was expecting this. In the same chapter, Kira says that her brother had also become a monk, and threatened her for being friendly with Rumata, a noble:
The boy also said that her brother had turned up—wounded, but cheerful and drunk, in a new uniform. He gave money to his father, drank with him, and was once again threatening that his boys would roll over everyone. He was now a lieutenant in some special squad; he’d taken the oath of allegiance to the Order and was about to be ordained. Father asked that she not come home under any circumstances. Her brother was threatening to settle scores with her for getting mixed up with a noble, the red-haired bitch.
Ibid, chapter 10.
However, it is unlikely that this was her brother, and entirely unlikely that this was some brotherly revenge or a random hit.
Another theory, originally published online, and the topic of the question by @DVK, Does the text support the theory that Arata the Hunchback killed this character?, suggests that it was Arata who ordered Kira's assassination, in order to provoke Rumata's anger (since Arata had subtly criticised Rumata for lack of action before). I feel that the answer I gave to that question is sufficient (and too long to quote here), but my main points are: Arata respected (and maybe even feared) Rumata; Reba had much stronger motivation; don Condor (being more experienced) had already predicted that Rea would try to use Kira; the attackers were monks, which implies they served Reba.
Also, it was clearly the authorial intent that Reba ordered the abduction, and it is worth noticing here that the whole chapter with Arata the Hunchback was added by authors after some advice by editors (due to censorship concerns), so it is unlikely Arata was intended to have a role other than simply being mentioned.