No Doubt, fronted by Gwen Stefani, is kicking off their Sphere residency in Las Vegas in a big way ... but Blake Shelton won't be there to watch his lady light up the stage ... TMZ has learned.

Sources with direct knowledge tell TMZ ... Blake is sitting this one out and not by choice, but because he's got his own gig at the exact same time. The country superstar is performing tonight at The Colosseum at Caesars Palace, down the street from Gwen.

Our sources say Blake is bummed to miss opening night, but fully plans to catch the show during its run once his schedule frees up.

As for Gwen's kids -- Kingston, Zuma and Apollo -- they’ll also be absent tonight. We’re told it’s simply a school night, and with classes in session, they’re staying put for now. The plan is for them to attend a later show when they don't have school the next day.

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We're told the band has been rehearsing around the clock to perfect their visually immersive show at the Sphere, which is already generating massive buzz. The residency is a limited run through June 13, built specifically for the high-tech venue.