As with many statutes, rules, regulations, etc. especially by the federal government, these statutes are spread throughout several codes. There is the Code of Federal Regulations and the United States Codes, both quoted below. I did my best to find all the applicable ones, but may not have succeeded. I simply have laid out the statutes, and am NOT offering any legal advice.
Federal Campfire Statutes:
CFR › Title 36 › Chapter II › Part 261 › Subpart A › Section 261.5
36 CFR 261.5 – Fire.
The following are prohibited:
(a) Carelessly or negligently throwing or placing any ignited substance or other substance that may cause a fire.
(b) Firing any tracer bullet or incendiary ammunition.
(c) Causing timber, trees, slash, brush or grass to burn except as authorized by permit.
(d) Leaving a fire without completely extinguishing it.
(e) Causing and failing to maintain control of a fire that is not a prescribed fire that damages the National Forest System.
(f) Building, attending, maintaining, or using a campfire without removing all flammable material from around the campfire adequate to prevent its escape.
(g) Negligently failing to maintain control of a prescribed fire on Non-National Forest System lands that damages the National Forest System.
[42 FR 2957, Jan. 14, 1977, as amended at 46 FR 33520, June 30, 1981; 73 FR 30307, May 27, 2008]
§ 261.1b Penalty
Any violation of the prohibitions of this part (261) shall be punished by a fine of not more than $500 or imprisonment for not more than six months or both pursuant to title 16 U.S.C., section 551, unless otherwise provided.
§ 261.52 Order
When provided by an order, the following are prohibited:
Building, maintaining, attending or using a fire, campfire, or stove fire
16 U.S. Code § 551 – Protection of national forests; rules and regulations
The Secretary of Agriculture shall make provisions for the protection against destruction by fire and depredations upon the public forests and national forests which may have been set aside or which may be hereafter set aside under the provisions of section 471  of this title, and which may be continued; and he may make such rules and regulations and establish such service as will insure the objects of such reservations, namely, to regulate their occupancy and use and to preserve the forests thereon from destruction; …
Once the order is in effect under 16 USC § 551 then the following penalties are provided:
18 USC § 3559 lists the classification of offenses and states: [when not specifically designated in the statute it is determined by its punishment] six months or less but more than thirty days, as a Class B misdemeanor
18 USC §3571, class B misdemeanor carries a maximum fine of $5000
18 USC §3581, class B misdemeanor is carries a maximum jail time of 6 months
I have an example of the 2014-2015 order I will post, probably tomorrow if events allow.