Drawing an Extra Card During Mulligan
Friday Night Magic runs at Regular REL, and is covered by Judging at Regular. The Tournament Rules and Infraction Procedure Guide cover Competitive and Professional REL. This answer borrows from all three documents and covers all three RELs.

Should I call a judge?

Absolutely.

Am I required to call a judge?

No. According to the Infraction Procedure Guide, it is acceptable for players to agree on a fix without calling a judge.


  If a minor violation is quickly handled by the players to their mutual satisfaction, a judge does not need to intervene.


Should a judge intervene if I don't call?

Judging at Regular describes that a judge should intervene, since you did something illegal.


  You should intervene if you see something illegal happen in a match, but beyond this you have a lot of room to tailor your actions. For example, whether you step in when you see a player miss a trigger should be determined by the tone you want to strike for your event – it may be appropriate to provide this extra help in a more causal environment, but not appropriate if your play group is more competitive.


This is reiterated in the Tournament Rules:


  Judges do not intervene in a game to prevent illegal actions, but do intervene as soon as a rule has been broken or to prevent a situation from escalating.


What is the ruling?

At Regular REL, you will simply lose the extra cards. They'll be shuffled back into your library. From Judging at Regular:


  If the identity of the card(s) were known to all players, return them to their proper location. Otherwise, determine how many extra cards have been drawn, take that many cards at random from the player’s hand and place them on top of the library. If the extra cards were drawn while drawing the opening hand, shuffle the extra cards back into the deck instead and allow the player to continue making mulligan decisions.


At Competitive or Professional REL, the ruling is different. You receive a warning, and then you have a choice. You may choose to allow your opponent to see your hand and remove cards equal to the excess number. If you do, then you can choose whether or not to mulligan. Otherwise, you must mulligan. From the Infraction Procedure Guide on Game Play Error — Mulligan Procedure Error:


  If the player has too many cards in hand, he or she may choose to reveal his or her hand, and his or her opponent chooses a card from it to be shuffled back into the library. If more than one excess card was drawn (for example, eight cards drawn during a mulligan to 6) his or her opponent continues removing cards until the correct number has been reached.
  
  If cards are not removed from the hand this way (either due to an error that didn’t lead to too many cards, or by the player choosing not to reveal), that player takes an additional mulligan.
  
  Players may continue taking mulligans after the remedy has been completed.


Examples:


You mulligan to six, but accidentally draw seven. You choose to reveal your hand. Your opponent removes cards equal to the excess (one card). You are left with six cards, and  and you retain the option to mulligan.
You mulligan to six, but accidentally draw seven. You choose not to reveal your and. You are forced to mulligan. You are left with five cards, and you retain the option to mulligan.