No procedure
Without an established procedure to deal with this type of incident, in

some cases, the referee will delay in asking the player to leave the field.

With or without prior direction the player must wait for a signal to

re-enter the field at the right time.
The recommendation below encourages referees to use a logical process to manage these situations. It’s not a definitive guide but can be used as a basis to follow for is done when a player is bleeding.

What to do
Normally, when one of these situations occurs, it is important for the referee to do the following: once the player is off the field he may re-enter if one of the officials finds that the injury has stopped bleeding. This is allowed prior to authorization from the head referee as long as there is a stoppage in play.
This may occur whether or not there are blood stains on the uniform. 

Blood stained uniform
If the player has a bloodstained shirt, generally he will be allowed to re-enter the field when there is a stoppage in play as long as; one of the assistant referees finds that his uniform has been cleaned with stains removed, the wound has stopped bleeding and the referee has authorized it.
Law 4 states that a player who has left the field must follow this procedure in having their equipment checked.

Uniform in order
However, there is an exception. If a player leaves the field with a bleeding injury but without blood stains on his uniform, he may re-enter the game, once an assistant referee has confirmed the bleeding has stopped, and the referee has given permission.

A player with a bleeding wound must be treated as an injured player again and can re-enter the game while the ball is in play, as long as the referee gives permission.