Airbus UK Broughton's Ryan Wade, 28, was banned for three "approved competition" matches from 21 April.
A hearing on 5 April found he "brought the game of association football or the association into disrepute".
Johnson, 28, was jailed for six years for grooming and sexual activity with a girl aged 15.
The former Sunderland player has lodged an appeal against his sentence.
BBC Wales understands the nature of the tweets was deemed offensive and were sympathetic towards Johnson.
The Welsh Premier League said the three-man panel sat at the headquarters of the Football Association of Wales.
Wade has been suspended from all football-related activity and fined Â£150, as well as a Â£50 contribution towards costs.
The club, based in Broughton, Flintshire, said in a statement: "The club carried out our own investigation and disciplinary process at the time and that has now concluded."
Wade signed for Airbus almost four years ago and has made 28 appearances this season, scoring four times.

Many have now taken refuge in the Evangelical Church in the Suez Canal city of Ismailiya.
The Coptic Church has condemned the attacks, saying they were aimed at "dividing" Egyptians.
On Sunday, Islamic State militants released a video, warning of more attacks on Egypt's Christian minority.
The Copts - who make up about 10% of the country's 90 million population - have often been targeted by Islamists in recent years.
Most of the Islamist militant attacks of recent years have been focused on the Sinai peninsula, where an IS-linked jihadist group is active, but the capital Cairo has also suffered a string of attacks in the past two years.
About 250 Christians with their belongings were now in Ismailiya's church, deacon Nabil Shukrallah said on Friday.
"They've come running with their children. It's a very difficult situation. We're expecting 50 or 60 more," he told the AFP news agency.
Meanwhile, refugees said they were now "scared of our shadows", adding that they "are being targeted in an ugly way".
Many of them were from the city of El-Arish, where at least seven Christians have been killed.
Egypt has seen a wave of attacks by militants since 2013 when the military overthrew President Mohammed Morsi, an elected leader who hailed from the Muslim Brotherhood, and launched a crackdown against Islamists.
Some of Mr Morsi's supporters blamed Christians for supporting the overthrow.
In December, a bomb explosion in the Coptic Christian cathedral in killed at least 25 people.
The Coptic Orthodox Church is the main Christian Church in Egypt. While most Copts live in Egypt, the Church has about a million members outside the country.
Copts believe that their Church dates back to around 50 AD, when the Apostle Mark is said to have visited Egypt. Mark is regarded as the first Pope of Alexandria - the head of their church.
This makes it one of the earliest Christian groups outside the Holy Land.
The Church separated from other Christian denominations at the Council of Chalcedon (451 AD) in a dispute over the human and divine nature of Jesus Christ.
The early Church suffered persecution under the Roman Empire, and there were intermittent persecutions after Egypt became a Muslim country. Many believe that continues to this day.
A Welsh Premier League footballer has been banned for tweets he posted after the trial of ex-England international Adam Johnson.
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Dozens of Coptic Christian families in Egypt have fled North Sinai province after a number of killings in recent weeks by suspected Islamist militants.