Kevin Costner Did Not Get 'Yellowstone' Set Member Pregnant, Despite Rumor

Kevin Costner has become the target of nasty rumors since his wife filed for divorce, including one accusing the actor of getting a woman working on the set of "Yellowstone" pregnant ... a tale we're told could not be further from the truth.

Sources close to Costner say the latest bit of gossip surrounding the star is "total BS," and has been baselessly circulating online.

It's unclear who started the rumor, or even who Costner allegedly got pregnant, but the fake story has been buzzing on social media since his wife, Christine, filed for divorce Monday.

One Twitter user wrote, "I wonder now, if the drama surrounding Kevin Costner and Yellowstone 'scheduling,' was due to the rumor of him potentially getting someone on set pregnant?" Another said, "So it wasn’t Bentley who got a girl pregnant on the Yellowstone set ... it was Costner."

TMZ broke the story, Costner was blindsided by Christine's filing ... the actor's rep made that clear in telling us, " ... circumstances beyond his control have transpired which have resulted in Mr. Costner having to participate in a dissolution of marriage action."

We're told Kevin had no prior warning Christine was filing to end their 18-year marriage, and he's still in the dark.

In her divorce docs, Christine lists the date of separation as last month -- they got hitched back in 2004. Interesting, since sources say Kevin had no inkling the marriage was ending.

Costner filed a response to the divorce petition in which the prenup is referenced requiring  Christine to vacate Kevin's 3 homes.