Not that it did, but if something stuffed up during the launch of a module, could it have been destroyed before hitting the ground?
Partial answer: The US modules* themselves did not, but their launcher (the Space Shuttle) did**
*The FGB is a "US module" in the sense that the US paid for it and owns it, but it was built, launched, and operated by Russia.
In general, payloads are not fitted with their own range safety systems since destruction of their booster is considered to be an adequate safeguard. The ISS modules were payloads.
I posted a long answer that focused on the launchers and not the payloads in error...I have re-included it below for links/info
So, in addition to the answer Organic Marble posted:
US ISS payloads: As per Organic Marbles answer.
Russian ISS payloads:
Split into two:
- Proton carried all large ISS modules: Zarya, Zvezda, and Nauka
- Soyuz carried smaller modules Prichal, Pirs, and Poisk
There was not a FTS as such (comparable to the US requirement) for both launchers, instead they both carried the same automatic system of 'engine cut-off' after sufficient boost from launch platform area, then let it fall to the ground (or burn up in atmosphere).
Since then, Soyuz launching from ESA Kourou were forced to be fitted with manual FTS.
Of note is that spacecraft such as TKS and Almaz did have self destruct and it has been used. Early Vostok and Soyuz craft also had self destruct charges.
Of note because Zarya and Nauka are based on the TKS spacecraft and Almaz bears similarity to Zvezda Service Module (though the latter is the DOS version so substantially, and comfortably, different), though whether the same systems were carried through to the ISS versions is unknown at this time, but considered highly unlikely.
(As Zarya is US-owned I find it unlikely that they would allow a Russian self destruct mechanism to be left in the design)
So, in reference to the OP's question of whether the ISS modules/payloads themselves had a self-destruct mechanism on board, the answer is likely: no.
All US launches are required to have FTS fitted (https://www.law.cornell.edu/cfr/text/14/appendix-D_to_part_417)
ESA and JAXA launches operate FTS.
Russia - sort of FTS. See below:
Construction of the ISS was pretty much from 1998 to 2011 with additional modules dropped and attached in 2021.
During that period the ISS launches were carried out with Russian (ie. Proton, Soyuz) and US launchers (ie. STS).
All US launchers had FTS as a requirement.
Russians do not have the same FTS - all large ROS ISS modules were launched by the Proton launcher, for which the FTS was to 'switch off the engines', and let it drop. Smaller launchers, such as Soyuz (with Soyuz or Progress, Prichal, Poisk payloads) have the same system in that they are directed away from the launch platform and then the engines are cut off (referred to as SBN (Booster Safety System)), and it is left to drop and impact the ground.
Given the geography it was felt that this was enough.
Soyuz also operates from ESA launch site at Kourou. For them to be able to do this they had to satisfy the FTS requirement and so Soyuz launchers from there have FTS fitted.
But these officials said they had bowed to French government demands that a manual launcher-destruct capability be added to the Soyuz’s existing automatic on board self-destruct system.
officials at the Soyuz production facility here showed visible irritation at the requirement, saying the current Soyuz safeguards have triple redundancy and needed no additional feature.
“We have been using a triple-redundancy safeguard system since the early days of Soyuz,” Baranov said. “The on-board software stops the vehicle’s engines in the event of a danger. It is completely automatic and has never failed. But we will do as the French government has requested, even though we are sure that no French launch director will ever react more quickly than the automated system already in place.”
Soviet (then Russian) spacecraft are known to have self-destruct mechanisms on board themselves, and these have been used. But this is not counted as part of a FTS.
Reference Almaz-T station self destruct:
12 April 1986 revived the Almaz program.
To the designers' surprise, the Almaz was in decent condition (in contrast to its fairing, which had been used as a toilet).
It had only been saved by its external placards - 'Warning - Don't Enter - Self-Destruct Charges on Board'.
This much-suffering Almaz was launched on November 29, 1986. But the second stage did not separate for the first time in many years and the same self-destruct charges destroyed the Almaz.
Of further note is that all large Russian ISS modules were able to fly autonomously, or under ground control, to their intended target/orbit. That is to say, they had their own engines, and as such, if required, they could be commanded to self-destruct via a fiery re-entry (For a large example, look at Mir's de-orbit in 2001).