Hobbes does address the idea of justice when speaking about Natural Law, however, justice enters only at a tertiary level. The primary components of Natural Law allow for neither justice nor injustice as every individual is said to be in a warring state with every other individual for full possession of goods and full dominance of territory. Hobbes says that primary passion and reason combine to compel individuals to seek a pleasant life (passion) and peace as know from "the laws of nature" (reason), thus driving him to seek contracts for secondary civility and escape from warring. Justice enters at the tertiary level as these contracts require enforcing through the offices of an agreed upon governing power.
The first law of nature, according to Hobbes, is thus to seek peace.
The second law of nature is thus to seek contracts of peaceful accord.
The third law of nature is then to honor and keep the contracts by governing against the injustice of violating contracts and encouraging the justice of keeping contracts.
Yes, even though justice as a concept is not necessarily directly addressed in this work, it is clear that the whole concept of a social contract necessitates some reference to justice in the way that we behave as we ourselves would want others to treat us to avoid the justice of having others treat us in a bad way, because if we treat others badly, they will only respond in the same way. Of course, we can see the origins of this theory emerging from Jesus' teaching in the New Testament.
I agree with the first post that justice does exist under Hobbe's system of government; but it is something of a de facto form of justice. Hobbes theorized that each person gives up certain rights to preserve the greater good; that is to prevent the "war of all against all." If a person refuses to abide by the rules of society, then he is liable to punishment to prevent the society from collapsing. All societies must have some form of enforcement; and that enforcement normally is denominated "justice," although those who are subject to its penalties might feel otherwise.
I would argue that justice does have a place in Hobbes's theory of the social contract. Of course, much of Hobbes's theory is driven less by issues of justice than by a simple desire for self preservation, but justice does play a part in Hobbes's vision of a social contract.
Hobbes argues in part that all of the laws of nature can be boiled down to one law. That law says that people should not do to others that which they do not want done to them. This certainly seems like a law that is motivated, at least in part, by a desire for justice.
Of course, one can argue that this law comes only from self-interest, but I would argue that it shows a concern for justice as well.