Shafqat Emmanuel and Shagufta Kausar were found guilty of sending the text message to the imam of their local mosque.
Allegations of blasphemy against Islam are taken very seriously in Pakistan.
Several recent cases have prompted international concern about the application of blasphemy laws.
The imam brought a complaint against the couple last July.
The couple’s lawyer said he would appeal against the sentences and said the trial had not been conducted fairly.
Pakistan has a de facto moratorium on the death penalty so it is unlikely the couple will be executed.
They come from the town of Gojra in Punjab, previously the scene of communal violence.
In 2009, the rumored desecration of a copy of the Koran led to a mob burning nearly 40 houses and a church in Gojra. At least eight members of Christian community died in the violence.
Since the 1990s, scores of Christians have been convicted for desecrating the Koran or blaspheming against the Prophet Mohammed.
While most of them have been sentenced to death by the lower courts, many sentences have been overturned due to lack of evidence.
Critics argue that Pakistan’s blasphemy laws are frequently misused to settle personal scores and that members of minority groups are also unfairly targeted.
Muslims constitute a majority of those prosecuted, followed by the minority Ahmadi community.
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