Yes

The beneficiary of a nondetection spell:

1. Can’t be targeted by any divination magic, and
2. Can't be perceived through magical scrying sensors.

There are only two spells in the PHB that create magical scrying sensors: clairvoyance and scrying. These are obviously covered by Item 2.

It's reasonable to assume that the remaining 28 spells from the divination school in the PHB, including true seeing, are covered by Item 1. They certainly fall into the category "any divination magic," so the question is, what does it mean to be "targeted" by these spells?

Does the spell have to explicitly refer to a "target" in its spell description? That's only two spells: the cantrip true strike and the 1st level ranger spell hunter's mark. This would be a very short list for a 3rd level spell, and neither of these is really a 'detect'-class spell. We need a broader definition for "targeted" than this.

It might be tempting to equate the target of a spell with the range of a spell; however, at least in the case of divination spells, this yields rather absurd results. Out of the 28 spells, 17 have a range of "Self," while another 4 have a range of "Touch" where the spell description specifies a willing creature. Clearly the recipient of these spells is not the one being "targeted" by them. Otherwise this would imply that a caster under the protection of nondetection, for instance, would not be able to cast spells like comprehend languages or speak with animals on themselves for the duration. That is clearly not the intent of the spell. Furthermore, even if a creature thought this was a desirable effect, they could avoid being "targeted" by 3/4ths of all divination spells simply by not casting them or by declaring that they aren't "willing."

In addition, if we assume that the target of a spell with range "Self" is the caster's own self, and not a creature one is trying to detect, then nondetection would provide no protection from detect evil and good or detect thoughts, which would seem to be exactly the kind of thing for which this spell is intended.

There is even a case to be made from RAW that target is not the same as range. Consider detect thoughts. It has a range of "Self," and it allows the caster to detect creatures they can't otherwise see. Yet the rules for Targets say (PHB 204): "Unless a spell has a perceptible effect, a creature might not know it was targeted by a spell at all. An effect like crackling lightning is obvious, but a more subtle effect, such as an attempt to read a creature’s thoughts, typically goes unnoticed." So the range of the spell is the caster's self, but the target of the spell is the creature having its thoughts read.

Since "target equals range" leads us to absurdity, I propose a simpler, alternative reading of the spell: the recipient "can't be detected by any divination magic or perceived through magical scrying sensors." If they can be detected by other means, fine; but if the only reason they can be detected is because of a divination spell, as is the case with an invisible creature who could be perceived with true seeing but is otherwise hidden, then they remain undetected.

The nondetection spell thwarts mind spike

The mind spike spell it a Divination spell and it has a target. Meanwhile, nondetection prevents you from being targeted by any Divination magic. If the rules wanted this to only apply to a certain subset of Divination spells, the rules would include text indicating that that is the case. Lacking such text, we know it applies to any and all Divination spells, completely indiscriminately.

Thus, nondetection means you cannot be targeted by mind spike, a Divination spell.