Three people were arrested (one outside the stadium and two inside) at the fixture played at Partick Thistle's Firhill Stadium in Glasgow.
The clash was also delayed at one stage for safety reasons to allow smoke to clear the pitch after both sets of fans let off flares.
Seats were also ripped up by fans inside the ground as they watched Rangers win the match 3-2.
Both clubs condemned the actions of their supporters.
A Celtic spokesman said: "We are looking into last night's match in more detail, together with all the relevant authorities, and clearly will deal with any issues appropriately."
A Rangers spokesman added: "It is disappointing that the off-field incidents at the Glasgow Cup Final last night detracted from a good game of football and a terrific result for the Rangers U17 team."
Police are currently looking at CCTV footage to try and catch those responsible for the trouble.
Celtic and Rangers' senior sides traditionally met at least four times a season but there was no fixture between the teams this campaign due to Rangers' relegation to the Scottish Third Division for financial irregularities.
- Sports & Recreation
- Partick Thistle