He also quipped: "I am very happy to visit this beautiful country with all its sheep."
Reddy said she was honoured to welcome Widodo and his delegation.
"Indonesia is one of New Zealand's oldest and closest partners in South East Asia. This year we celebrate 60 years of diplomatic relations."
Earlier Widodo paid his respects at the Tomb of the Unknown Warrior at the Pukeahu National War Memorial, where a lone protester was heard repeatedly yelling "Free West Papua".
Ardern has been urged to raise the issue of West Papua, which had been fighting for independence from Indonesia, in her bilateral meeting with Widodo this afternoon.
"West Papuan people have been seeking freedom from repressive military rule. The loss of life is estimated to be at least 100,000," West Papua Action Auckland said in a statement.
"Our Melanesian neighbours in West Papua are suffering grievously and must not be overlooked for the sake of 'good relations', or markets for our goods."
Widodo and his wife, Iriana Joko Widodo, were greeted at Pukeahu by Defence Minister Ron Mark, former chief of navy Rear Admiral David Ledson, Chief of Army Major General Peter Kelly and Air Vice-Marshall Robin Klitscher.
Widodo laid a wreath on the sanctuary steps in the Hall of Memories.
A minute's silence was held, following a reading of the Ode of Remembrance.
Widodo, his wife and Mark then laid a fern on the Tomb of the Unknown Warrior.
Widodo is the head of the country with the world's largest Muslim population, and the largest economy in the Association of Southeast Asian Nations (Asean). It is a major market for New Zealand meat, dairy and agriculture exports, with total two-way goods trade of $1.76 billion in 2017.
He arrived in Wellington last night to a rousing welcome from local Indonesians, after attending an Asean meeting in Australia at the weekend. It is his first visit to New Zealand, and he is accompanied by his wife, ministers and a business delegation.
The delegation was officially welcomed to New Zealand in a ceremony at Government House in Wellington this morning. He was met on the grounds by kaumatua Professor Piri Sciascia and kuia Hiria Hape, before accepting the wero (challenge) from the NZ Defence Force Maori Cultural Group.
This was followed by a rousing haka from 50 students from Wellington College, led by students Geordie Bean and Sean Howe.
Reddy then greeted the delegation and accompanied them as they met students from Scots College Preparatory School and Newlands College, and then inspected the 100-strong tri-service Guard of Honour.
Members of the diplomatic corps were also on hand to meet Widodo and his delegation.
Widodo first met Ardern at the East Asia Summit last year and will have a bilateral meeting with her this afternoon.
It is customary for visiting heads of state to hold a press conference after meeting with the Prime Minister, but it is understood Widodo requested that no press conference be held.
It will mean he will not be opened up to questions from media, including about West Papua.
Widodo is also meeting with Opposition leader Simon Bridges.
Trade is expected to be high on the agenda; a booming population and consumer class make Indonesia an important market for New Zealand.
New Zealand and Indonesia have free trade through New Zealand's trade agreement with Asean, but in 2013 New Zealand took Indonesia to the World Trade Organisation over 18 agricultural trade barriers.
According to the Ministry of Foreign Affairs and Trade, the barriers are estimated to have cost the New Zealand beef sector up to $1b, and have also affected horticultural exports.
Indonesia appealed a decision in New Zealand's favour in 2016, and the WTO upheld its ruling in November last year that the 18 barriers were inconsistent with global trade rules.
Trade Minister David Parker said at the time of the ruling that it would open the way for further export growth to Indonesia.
