Rowe, 24, has signed a contract until 2020 but will not available to play for the Suffolk club until Tuesday's league game against Derby County.
He has scored six goals in 25 National League appearances for Macclesfield this season and helped the Silkmen to the second round of the FA Cup.
Rowe is the fifth new addition made by boss Mick McCarthy in January.
Striker Kieffer Moore, defender Jordan Spence and centre-back Steven Taylor have all signed full-time deals, while midfielder Toumani Diagouraga has joined on loan from Leeds until the end of the season.
Find all the latest football transfers on our dedicated page or visit our Premier League tracker here.

The vessels, found by archaeologists at Must Farm near Peterborough in 2011, have now been dated to about 1500 BC, 200 years older than was first thought.
Samples taken during the conservation process have revealed the boats to be made from oak, lime and field maple.
The vessels are undergoing a two-year preservation programme at Flag Fen.
The wooden craft are being sprayed with a special wax to stop the timbers from degrading, the same technique that was applied to the 16th Century Mary Rose warship.
It is hoped the process will reveal more about the Must Farm log boats, one of which is almost 30ft (9m) long.
Mark Knight, from Cambridge Archaeological Unit, said: "We've been carbon dating the sediment the boats were found in to try and create a detailed chronology of the river channel that once ran from the Midlands to the North Sea.
"This will tell us when each of the boats were disposed of by the people of the time.
"What we're now working on is carbon dating the actual boats which will give us an idea of when they were constructed.
"This will then tell us how long they were in use and gives us a much greater depth to the history of the area."
Visitors to Flag Fen will be able to watch conservators at work, with the aim of eventually putting the boats on public display in glass cabinets.
Mr Knight said: "As we lack any texts from the time to tell us what was going on, the boats help us to better understand the levels of craftsmanship and technical sophistication of the time.
"In the future we'll be judged by the technology we leave behind and these boats are a similar marker for the people of the Bronze Age."
See more on the boats of Must Farm on Inside Out East, Monday at 19:30 on BBC One and for seven days after on the iPlayer.

The long-term proposals for Hay Castle in Hay-on-Wye would allow it to open to the public for the first time.
Hay Castle Trust has been awarded £528,600 to help develop the plans which include an arts centre.
The castle was built in the late 12th Century by the powerful Norman Lord William de Braose.
It was sacked the following century and rebuilt by Henry III.
Castle House, the adjoining Jacobean mansion, was built in 1660 but was severely damaged by fire in 1939 and 1977.
The castle has been owned by Richard Booth, the man credited with transforming Hay into a global attraction for second-hand book lovers, but was purchased in 2011 by the Hay Castle Trust.
The Heritage Lottery Fund said the grant would help the trust to develop its plans.
It eventually hopes to secure more than £4.8m to put towards proposals which include conserving the medieval and Jacobean buildings, and creating a new centre for arts and culture.
Championship club Ipswich Town have signed Macclesfield Town winger Danny Rowe for an undisclosed fee.
[NEXT_CONCEPT]
Eight Bronze Age boats discovered in a deep Cambridgeshire quarry are much older than it was first thought, carbon-dating research has revealed.
[NEXT_CONCEPT]
A medieval castle which stands over a Powys town is to receive more than £500,000 as part of plans to restore it.