Most Revd Justin Welby said Eid Mubarak, or happy Eid, referring to the time of feasting and celebration after their annual thirty-day fast.
During Ramadan, Muslims fast from sunrise to sunset for thirty days, to become closer to Allah (God) and to show solidarity with the poor, who often have no choice as to whether they go hungry or not.
The Anglican leader also said he has been praying for Muslims who have been "greatly on his mind" during Ramadan.
He referred to the physical difficulty of Ramadan, particularly during the Summer heat, but also the pressure on the Islamic community in light of recent terrorist events in Kuwait, Tunisia and other countries.
Mr Welby also reiterated his and the church's love for Muslims as brothers and sisters in humanity, while stressing the need to openly acknowledge and discuss the differences the two faiths have.
Catriona Robertson, director of the Christian Muslim Forum who also took part in Ramadan in solidarity, told Premier's News Hour: "Eid is the end of... [Ramadan], so there's a lot of partying and feasting and coming together. It's a great time of celebration.
"I really like receiving greeting cards at Christmas time from my Muslim friends. I think it's lovely for Christians to be able to say "Eid Mubarak" to our Muslim friends just as our Archbishop did.
"I was really pleased to see the Archbishop of Canterbury's video message greeting this morning, and also the Prime Minister's video message to the Muslim community last night.
"The Archbishop used the phrase 'under pressure', that the Muslim community's under pressure at the moment, because of what's happening overseas. Many of my Muslim friends were particularly upset that a link was claimed with Islam for the shootings in Tunisia and Kuwait, just during this very holy month.
"So to be able to reassure our Muslim friends that we're still our friends, just like the Archbishop did, and work together for the common good, I think is something useful we can do as Christians."
Listen to Premier's Des Busteed speaking to Catriona Robertson here:
