Four singles were released from the album: "Si Tú Supieras", "En El Jardín" (a duet with Gloria Estefan), "No Sé Olvidar", and "Yo Nací Para Amarte".

Upon its release, Me Estoy Enamorando was met with positive reviews from music critics who praised Fernández's vocals, Estefan's productions, and Santander's songwriting.

[1] Estefan herself makes a guest appearance on the duet track "En El Jardín", a "glorious ballad on the moment love is born".

[9][10] Its third and fourth singles, "No Sé Olvidar" and "Yo Nací Para Amarte," also reached number one on the same chart holding that position for eight and five weeks respectively.

[16] To promote Me Estoy Enamorando, Fernández launched his first solo tour performing in Argentina,[17] Central America,[18] Mexico,[19] and the US.

[21] His set list consisted of rancheras from his past recordings, several tracks from Me Estoy Enamorando, and a Spanish-language rendition of Frank Sinatra's "My Way".

[22] Reviewing his concert at the Universal Amphitheatre in Los Angeles, California, Los Angeles Times editor Ernesto Lechner felt that Fernández "seemed to suffer from the same malady that affects most modern Mexican pop stars", citing "Si Tú Supieras" and "No Sé Olvidar" as "unnervingly soulless".

[20] Alejandro Riera of the Chicago Tribune commented that Fernández has "one mean set of pipes" and "used that voice to successfully seduce just about everybody in his mostly female audience".

Riera also noted that unlike his father, Vicente, who sings "the tequila-drenched songs of unrequited love", Alejandro "praises the power that women hold over men.

AllMusic editor Terry Jenkins gave the album four-and-a-half out of five stars, calling it a "fine romantic record".

[25] Mario Tarradell of The Dallas Morning News felt that Fernández's vocals "caresse... every song on Me Estoy Enamorando" and praised his delivery.

On the title track, he compared Fernández to Mexican ranchera singer Javier Solís: " Like Solis, Fernandez can whisper soft and compassionate requests for requited love, and belt out tortured sobs of pain while still retaining a macho posture that says, 'Yes, I'm crying, but I'm not giving up'.

"[5] Knight Ridder music critic Howard Cohen gave the album four out of four stars lauding Fernández's vocals and Estefan Jr.'s production.

[1] Ramiro Burr's review for the San Antonio Express-News praised the "blend of pop balladry with ranchera rhythms and traditional instruments that elevates this CD".

He felt that Fernández "conveys a wealth of emotion in his songs" and called "En El Jardín" a "glorious ballad".

[6] Eliseo Cardona of El Nuevo Herald lauded Santander's compositions and called Fernández a "first-rate interpreter who knows how to give a poetic edge to everything that goes through his throat".

[26] At the 40th Annual Grammy Awards in 1998, Me Estoy Enamorando was nominated for Best Latin Pop Performance but lost to Romances by Luis Miguel.