More precisely, apart from modal verbs, is "wissen" the only non-modal verb that uses the same form for the 1st and 3rd person singular in Präsens? I can't think of any other verb that does this and I couldn't find any info online. If this were the case, it would be kind of curious I think.
I suppose you wouldn't be satisfied with a simple "yes", so a bit of context: I'm not sure how much you have thought about the conjugation of wissen (and of the modal verbs dürfen, müssen, etc.), so you might have already observed that their present indicative is formed like the strong verb preterite. Compare:
- sang, sangst, sang - sangen, sangt, sangen
- weiß, weißt, weiß - wissen, wisst, wissen
This is no coincidence. The behaviour is known as "preterito-present". In a nutshell, some Indo-Germanic perfect forms were - very early on - re-interpreted as present forms as their meaning changed and/or as they were fit into a new, evolving temporal system. For instance, wiȥȥen - generally assumed to be the oldest preterito-present there is - used to mean something like "having observed" (which points to a past action), but then increasingly assumed the meaning "know" (which points to the resulting, present state). So, essentially, the perfect forms continued to be used but they were now, in fact, present tense forms. (Not all of the other preterito-present verbs had such a change in meaning, but all of them shared that (past) action vs. (present) result ambiguity.)
For reasons that would go way beyond the scope of this reply, the (morphological) status as a preterito-present verb, beginning in Old High German, increasingly coincided with the (semanto-syntactic) property of being a modal verb, to an extent that at some point, the preterito-present full verbs lost their preterito-present property - wissen happens to be the only one that survived. And that is how we ended up with the status quo.