Henry Eben Burnham (November 8, 1844 – February 8, 1917) was a United States senator from New Hampshire.

[1] He attended the public schools and Kimball Union Academy and married Hannah Elizabeth Patterson.

Burnham graduated from Dartmouth College in 1865, studied law, was admitted to the bar in 1868 and commenced practice in Manchester.

He engaged in banking and insurance and was member of the New Hampshire House of Representatives in 1873-1874, was treasurer of Hillsborough County from 1875 to 1877, was judge of probate for Hillsborough County from 1876 to 1879, and was a member of the State constitutional convention of 1889.

He resumed the practice of law and died in Manchester on February 8, 1917; interment was in Pine Grove Cemetery.