You can generate JSON object using standard SELECT query with FOR JSON clause and WITHOUT_ARRAY_WRAPPER option, and insert it into JSON text as a third parameter:
declare @json nvarchar(4000) = N'{"Id":17,"Name":"WWI"}'
set @json = JSON_MODIFY(@json, '$.table',
JSON_QUERY(
(select name, create_date, schema_id
from sys.tables
where name = 'Colors'
FOR JSON PATH, WITHOUT_ARRAY_WRAPPER)))
print @json
(1 row(s) affected)
{"Id":17,"Name":"WWI","table":{"name":"Colors","create_date":"2016-06-02T10:04:03.280","schema_id":13}}
FOR JSON with WITHOUT_ARRAY_WRAPPER option may generate invalid JSON text if SELECT query returns more than one result (you should use TOP 1 or filter by primary key in this case). Therefore, JSON_MODIFY will assume that returned result is just a plain text and escape it like any other text if you don't wrap it with JSON_QUERY function.
You should wrap FOR JSON, WITHOUT_ARRAY_WRAPPER query with JSON_QUERY function in order to cast result to JSON.