Alexander Baker (1582–1638), was an English Jesuit.
He entered the Society of Jesus about 1610 and was professed of the four solemn vows in 1627 and visited India twice as a missionary.
Baker died on 24 August 1638 in London, where he had resided for many years.
Among the State papers is a manuscript by Baker in defence of the doctrine of Baptismal regeneration as held by Catholics, showing its difference from the opinion of Protestants.
This article about an English Roman Catholic cleric is a stub.