The damage will remain 2d6 if the save is failed.
Where a spell effect calls for a saving throw, critical damage is not in play. Reviewing spells like lightning bolt, fireball, and thunderwave that have multiple dice for damage, nowhere does the spell effect describe a doubling of damage dice for critical hits.
Hit or miss, the shard then explodes. (p. 19 Elemental Evil Player's Companion)
What this indicates is that the explosion damage is not linked to the attack roll's success or failure, and thus cannot benefit from the auto hit or critical on a 20, nor the auto miss on a 1. (p. 194 PHB)
Ice knife is an unusual spell in that it has two separate effects. One effect is an attack roll (hit or miss, and thus eligible for a critical hit benefit), while the other effect is the standard save versus damage.
Compare to other elemental spells
As a point of comparison, see this last part of the spell description (p. 19 Elemental Evil Player's Companion):
At Higher Levels. When you cast this spell using a spell slot of 2nd
level or higher, the cold damage increases by 1d6 for each slot level
This is comparable to Lightning Bolt's similar "at higher levels" language. From PHB p. 255:
At Higher Levels. When you cast this spell using a spell slot of 4th
level or higher, the damage increases by 1d6 for each slot level above
That elemental spell effect is also influenced by a saving throw and has no "critical" hit feature.