Probably not. It seems very unlikely.
First of all, India is quite a multicultural society with hundreds of various creeds and lots of religions. There is a longstanding tradition of being tolerant to other religions.
Also, there is very little antisemitism in India, see the quote at the bottom of this answer.
Moreover, I don't think many people would notice and care that you are Jewish. I've met lots of Israelis in the Indian town I live in. My experience is that the local people mostly just regard them as Westerners, and not particularly as Jews. I personally think this would be the case even if they were to wear kippahs, etc. I know the local language, and the same words (Westerner, foreigner, white person) are used whether they are referring to an Israeli, Norwegian or Australian. This is also the case if they know the person is Jewish or Israeli. So, I don't think they even think of Jewish people as a group distinct enough for it to matter.
Of course, lots of Indians will recognize a kippah and other Jewish marks and know what they mean, etc. But the mentality here is just not one where people care about such things. It's such a diverse society already.
The common mentality here is to keep one's own religion and traditions to oneself and let others keep theirs.
I agree with Nikhil's comment that it would probably be somewhat unwise to walk around in a large-city Muslim neighborhood dressed in orthodox Jewish attire in the middle of the night. But that's a rather extreme example. Also, I think even that would probably be fine, though. The vast majority of Muslims in India are very polite, friendly and like to mind their own business. I don't think they'd even care if an orthodox Jew walked through their neighbourhood. To err on the side of caution, though, perhaps there are wiser ways to spend one's holiday. So, let's forget about the extreme example.
Large numbers of Israelis and other Jewish people travel as tourists in India every year. I'm not aware of even a single case of religiously or ethnically motivated harassment of Jewish travelers by Indians. (If it occurred, it was probably just because they were foreigners, not in particular because they were Jewish. But note that Westerners are also generally treated very well, so even that would not be a common or big problem.) Most Jewish people traveling in India probably don't wear kippahs or otherwise look obviously Jewish, but I don't imagine it would be a problem even if they did. To be honest, I think they'd be treated pretty much like other Westerners. (Respectfully.)
I personally know an elderly Russian Jewish man who visits India every year, and he always wears a special Jewish hat (I don't know exactly what it's called, only that it's not a kippah). I'm not aware that being Jewish has been a problem for him even a single time.
If you're worried about it, you can avoid discussing religion and politics while you're in India. However, I think even this would mostly be fine. As long as one doesn't go around invasively preaching or getting into theological or political arguments, it should be absolutely fine. I see India as a very religiously tolerant country.
Frankly, I'd be slightly more concerned if you were a Muslim (even though India has a large Muslim population), but even that would mostly be totally fine.
Source: Having lived and traveled in India for five years and talked to many Jewish and Israeli tourists and expatriates about their experiences here.
If you try to google "antisemitism India", you'll find nearly no contemporary examples. (And not much of signifigance historically either.) There's a 2010 article from the Jerusalem Post called 'We are not frightened, there is no anti-Semitism in India'. The background for that article was that there had been a bombing of a German bakery in Maharashtra and there was speculation that a Jewish religious center down the street might also have been a target. However, the article presented it as a mere possibility and not a fact.
Rachel Kupchik, the leader of the religious center, noted:
India is a country with absolutely no anti-Semitism. There never was, and there isn’t now. Unlike in some European countries, where you have to hide the fact that you’re Jewish, here in India being Jewish generates respect.
While we should generally be careful with blanket statements such as these, I think Kupchik's sentiment is mostly correct. And she is clearly in a position to know, as a long-time Jewish resident of India who interacts with other Jewish people in India on a regular basis. On a side-note, I'm also unsure of which European countries she's referring to, but she might have meant some isolated areas in some European cities.