I would think the requirement of citizenship is implied...we don't give foreigners other constitutional rights like voting in our elections.
Actually citizenship is not implied because the Constitution did not define citizenship (14th Amendment) when the 5th Amendment was ratified. There was no Constitutional way to determine who was a citizen when the 5th Amendment due process rights took effect.
Furthermore, voting is not expressly a constitutional right. The states determine the qualifications for voters. The only thing the Constitution says is that qualifications for an elector for the U.S. Congress and the electoral college cannot be more stringent than the qualifications required for the larger branch of the electors state legislature and no person can be disqualified as an elector because of age (if they are over 18), gender, race/previous condition of servitude or failure to pay any tax.
BTW: We do give illegal aliens due process rights, i.e., they cannot be jailed or deported without appearing before a judge or being tried in court even though they are not U.S. citizens.