"Any Time, Any Place" received positive reviews from music critics. Billboard editor Andrew Hampp, while reviewing the album on its tweitheth anniversary, called it "a stone-cold classic". Sal Cinquemani from Slant Magazine noted that the song "provides a genuine climax: It's an oozing, slow-paced romp".Philadelphia Daily News 's Chuck Arnold called the song a "delicate, aching ballad", which "warmly climaxes the carnality with a cooing vow of insatiability".
The song held the number-one position on the BillboardHot R&B/Hip-Hop Songs for ten weeks (a record at the time) and became Jackson's biggest hit on the chart; it also peaked at number two on the Billboard Hot 100 (behind All-4-One's "I Swear"), while it saw limited success in Europe and Australia. With the song reaching number two on the Billboard Hot 100, Jackson became the only artist to release 3 consecutive albums with at least 5 top-ten singles in the U.S.
The video for "Any Time, Any Place" was directed by Keir McFarlane. Jackson is depicted playing sex games with a man across the hall. The video acted as a safe sex campaign. An alternate version of the video with the R. Kelly Mix was also shot with more explicit footage. At the end of the video, the screen fades to black, and a message fades in: "any time, any place ......be responsible".
Jazz musician Tom Scott covered the song in 1995 from the Night Creatures album.
Hip-hop artist Da Deputy sampled the song in 2012 with "Private Resort"
Kendrick Lamar sampled the song for his single "Poetic Justice", which featured Drake, and was titled after the film of the same title starring Jackson and Tupac Shakur. The song was released as the second single from his album Good Kid, M.A.A.D. City. A freestyle over the song's instrumental was recorded and released by American rappers Busta Rhymes and Q-Tip on December 21, 2012, where the two pay homage to the singer. The song's producer Scoop DeVille recalled several artists wanting the song based on the Janet sample, including rapper 50 Cent, before he ended up giving it to Lamar. DeVille discussed the idea for the sample, saying "The way that 'Poetic Justice' came about, we were in the lab, working. I heard the record on the radio. When I hear certain things, it moves you in a certain way. It's like emotion," he explained. "When you hear a certain song come on the radio, it's like, oh my goodness, this is crazy for it to be around that time. That record is one of the sexiest records of our time. Growing up, it was just a big record. Hearing it the way I did, I thought it would be crazy if I flipped it." Kendrick asked Jackson to appear in the music video saying it would be "a blessing" and he was "a young boy that looked up to you for years". Although interest was expressed she was unable to make an appearance.