There's a few lines that point to such, specifically Mika's infamous "How I wish to be touched by him, even if it's so hard that it hurts" idol story line that can be used to be like yeah this is masochism. I think Mika suffers from self esteem issues + the need to be "useful" to Shu, and coupled with Shu's tendancy to be verbally harsh with him especially in ! era it can come across like they're in some sort of sadomasochistic partnership. Even Naru makes a comment in Victoria that she initially assumed their relationship was the "dangerous/immoral" kind, which could be an allusion to this.

I feel like when looking at Mika from a psychologically masochistic angle, his self esteem plays a big part of it. He's not getting any gratification from beating himself up, but he feels like he deserves it. He doesn't really have a good view on "humanity" and believes it's flawed. Though Mika does enjoy the occasional praise as well, when he also feels it's deserved. In Victoria he asks Shu to praise him more and gets all nuzzled up to him in public, which Shu yells at him because it's hot and they're sweaty. In Teddy Bear, chapter 5 summarizes the extent to which Shu's harsh tone has a psychological affect on Mika. He mentions that everything rude/harsh Shu says about him is "technically true" and that he deserves it, while simultaneously feeling anxious that Shu is starting to be nicer to him, saying that Shu "must be getting ready to throw him away". I'd say this is definitely some form of psychological masochism, Mika not letting things get better because he's clinging on to the previous harshness as the norm, while feeling like he deserves that harshness no matter how it makes him feel.

As for the physical side of things... You could make the argument that Shu does get physical sometimes. There's a line in Marionette where Nazuna thinks that Shu might hit him, and then in Victoria the reason Mika has Mademoiselle in the first place is because Shu had an outburst and was throwing things around and Mademoiselle could have gotten hit, and he does throw a stuffed animal at Mika in Cheval Live. I personally think throwing soft things at Mika is as far as he's gone, or maybe getting a little bit too rough with helping Mika stretch / massage. There's also that line from Shu going "you! how about I stip you naked!" in Antique Legends to which Mika has sort of an amicable reaction to it.