Sounds like a joke, but in fact asking for a friend who is not a musician. Was there ever a "Concerto Piccolo" or some such contrast to the "Concerto Grosso" format?
In the term concerto grosso the grosso refers to the full orchestra, the ripieno. The orchestra is contrasted with a group of soloists. That group is called the concertino.
That contrasts with the term solo concerto or just plain concerto where there is only a single soloist.
In either case the full orchestra is called the ripieno.
It's kind of tricky terminology. Grosso is about the orchestra, but the full terms concerto grosso and solo concerto contrast the size of the solo(ists.)
The meaningful opposite of concerto grosso is simply solo concerto in the sense that the meaningful part is the size of the solo group.
Concerto grosso and concertino are opposite within the meaning of concerto grosso in that the large orchestra is contrasted against the concertino, the two groups sort of oppose each other.
There really isn't an opposite with this - like darkness is the opposite of light - so I wouldn't get hung up on one single notion of 'opposite.'
The first reference given in wikpedia has it concise:
"Concerto grosso" originally signified the "large consort," that is, the orchestra, as opposed to the "concertino" or "little consort," the group of solo instruments. Later, the term "concerto grosso" was applied to the composition which used these opposed groups.
The instrumentally smaller precursor was the trio sonata.
That being said, the question is mostly caused by the strange name (if the repertoire is meant.) It is not very different from asking for the opposite of a symphony. (Chamber music?)
Linguistically, the opposite of a Concerto Grosso would be a Concertino. Wikipedia defines it as
Concertino is the diminutive of concerto, thus literally a small or short concerto.
...and lists dozens of examples.
In terms of the structure and lineup of a concerto grosso, Wikipedia notes
The concerto grosso [...] is a form of baroque music in which the musical material is passed between a small group of soloists (the concertino) and full orchestra (the ripieno or concerto grosso). This is in contrast to the solo concerto which features a single solo instrument with the melody line, accompanied by the orchestra.