Cameron White top-scored for Victoria with an unbeaten 82 in their chase of 172, as the undefeated Bushrangers won with 4.1 overs remaining despite some late scares.
Warner, who scored just four in his only previous start for the Blues this season, is scheduled to meet with NSW Cricket chief executive Andrew Jones on Tuesday after he was a no-show for his Sydney grade side Randwick-Petersham on the weekend.
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After NSW won the toss and elected to bat, Warner was the first wicket to fall after facing 12 deliveries, chopping an attempted cut shot onto his stumps from the bowling of Scott Boland (3-42).
And there were few positives for NSW as Victoria consolidated their grip on top spot on the ladder with a third win from as many starts.
Victoria captain Matthew Wade did his national selection chances no harm with a stylish 50 scored off 64 balls in a match-high partnership of 110 with White for the third wicket.
Wade's dismissal kick-started a mini-collapse of 3-3, with wickets falling in quick succession as they had done throughout the match.
"It was a hard slog on that wicket," said White.
"The pitch was low and slow and if you bowl stump to stump it is quite difficult to score."
NSW won their opening match against Tasmania by 81 runs last week but sorely missed the services of Moises Henriques, Nic Maddinson and Brad Haddin who have departed for Australia's one-day tour of India.
The Blues crumbled to 3-19 and, although captain Steve Smith hit 47 off 73 balls, the run-rate remained modest throughout and the home side lost three further quick wickets to slip to 6-85 against a disciplined attack.
Ben Rohrer played a steady knock to top score for NSW with 63 off 91 balls on a slow wicket not conducive to big scoring.
Rohrer said Warner is unlikely to be troubled by a lack of confidence despite his successive failures.
"I thought he was a little unlucky to chop on," Rohrer said.
"He is normally good on the sub-continent type wickets, where they are low and slow and he hits the ball through point.
"He is never short of confidence so I'm sure he will enjoy going to Hurstville Oval next week where he made a massive score a few years ago."