Fernandez started each of Chelsea's first three Premier League games of the new season against Manchester City, Wolverhampton Wanderers and Crystal Palace.
The 23-year-old also featured in Argentina's recent World Cup qualifiers, starting with a win against Chile and a defeat to Colombia.
However, he was absent from the Chelsea squad when the team was released prior to Saturday's meeting with the Cherries.
In Fernandez's absence, summer addition Renato Veiga was given the opportunity to partner Moises Caicedo in the middle of the park.
Why did Enzo Fernandez miss Bournemouth clash?
Speaking prior to the game, Chelsea boss Enzo Maresca confirmed that Fernandez and fellow midfielder Kiernan Dewsbury-Hall were ruled out due to illness.
Maresca told Sky Sports: "The reason why is because him (Fernandez) and Dewsbury-Hall have unfortunately both been ill."
Despite being without the midfield duo, Chelsea went on to claim their second victory of the Premier League season.
Robert Sanchez kept out Evanilson's first-half penalty to keep the score goalless before Christopher Nkunku scored an 86th-minute winner after being played through by debutant Jadon Sancho.
Fernandez aiming to recover for West Ham encounter
After missing the trip to the South Coast, Fernandez will now be looking to recover in time for Chelsea's next fixture.
The Argentine has a week to overcome his illness, with Chelsea set to make the short trip to the London Stadium for Saturday's clash with West Ham United.
However, it remains to be seen whether Maresca would offer Fernandez an immediate recall even if he can prove his fitness in time for next weekend.
Fernandez's replacement Veiga played the full duration of Saturday's win and may have staked a claim to keep his spot in the side.