No, the ICJ does not have jurisdiction for something like this. You can check out the list of cases they dealt with; they are disputes between states. Who'd complain here? Iran against Iran?
Sometimes the UN refers some other cases to the ICJ for advisory opinions, but they at least involved more widespread allegations of human rights violations, albeit more indirectly. A single murder or manslaughter case is very unlikely to reach that bar. In any case, it would be an advisory opinion.
No comment on whether some other cases in Iran, taken together might qualify, since UNGA referrals are themselves somewhat political. There is one example I know of of Sweden claiming universal jurisdiction against an Iranian prison official, but that's not the ICJ who took action.
OTOH you may be confusing ICJ with the ICC, The International Criminal Court, which might have jurisdiction, but again there would probably have to be widespread incidents like this to qualify for an ICC investigation/case. The ICC is much more contested in international affairs. Iran themselves signed but did not ratify the Rome Statute. I'm not too sure what their current position is vis-a-vis of that court, i.e. whether they'd be remotely cooperative with an ICC investigation (esp. since the US doesn't have the best of records on that.)